Numericals Class - IX TMH.docx

UNSOLVED NUMERICAL PROBLEMS

1.A body moving with a speed of 36 km/h is brought to rest in 10 s. What is the negative acceleration and the distance travelled by the body before coming to rest?

2. A train starts its journey from station F; accelerates at the rate of 2 m/s2, and reaches its maximum speed in 10 s. It maintains this speed for 30 mm and retards uniformly to rest at the station Q after the next 20 s. Calculate:(a) The maximum speed of the train.(b) Retardation(c) The distance between stations P and Q.

3. A body travels 200 cm in the first 2 s and 220 cm in the next 5 s. Calculate the velocity at the end of the seventh second from the start. (Ans. 2.22 m/s)

*4.Robbers in a car travelling at 20 m/s pass a policeman on a motorcycle at rest. The policeman immediately starts chasing the robbers. The policeman accelerates at 3m/s2 for 12 s and thereafter travels at a constant velocity. Calculate the distance covered by the policeman before he overtakes the car.

5. Interpret the velocity-time graphs (Figs 1.16 and 1.17)Ans. No acceleration; uniform acceleration

Fig. 1.16Fig. 1.17

6. In Fig. 1.18 the position of a body at different times is shown. Calculate the speed of the body as it moves from A to B, B to C and C to D. Ans. 1 cm/s; 0; 2 cm/s

*7. A body is coming down an inclined plane with an acceleration of 1 m/s2. If it starts from rest, find the time after which its velocity becomes 5 m/s. Ans.5 s

8. The motion of a moving train has been depicted in Fig. 1.19. Find(a) The average velocity of the train in time OA.(b) The total distance covered by the train from 0 to D.(c) The uniform acceleration and retardation of the train.Ans. 6 m/s; 1860 m; 6 m/s, 5 m/s2

Fig. 1.19

*9. A body is dropped from a balloon which is moving upward with a speed of 10 m/s. The body is dropped when the balloon is at a height of 390 m from the surface of the earth. Find the approximate time taken by the body to reach the surface of the earth. Take g = 10 m/s2. Ans. 10 s

10. If a force of 15 N acts on a body in the direction of north and another force of 10 N simultaneously acts on it in the direction of south, what is the resultant force acting on the body? Ans. 5N towards north

* 11. A body is moving with uniform acceleration, and describes 75 m in the 6th second and 115 m in the 11th second. Show that its moves 155 m during the 16th second.

12. (a) A body is dropped from the roof of a building 10 m high. Calculate the time of fall, and the speed with which it hits the ground. Take g = 10 m/s2.Ans. 1.4 s; 14 m/s

(b) A ball is thrown vertically upwards with a velocity of 20 m/s. How high did the ball go? Take g = 9.8 m/s2. Ans. 20.4 m

13. A bicycle moving with a velocity of 3 m/s speeds up with an acceleration of 0.5 m/s2. What will its velocity be after 5 s and how far will it have moved during this time.Ans. 5.5 m/s, 21.25 m

*14. A ball is thrown vertically upwards. It reaches its maximum height in 2.5 s. If the acceleration of the ball 10m/s2 be directed towards the ground, find the initial velocity of the ball. Ans. 25 m/s

15. A scooterist is racing at a speed of 72 km/h. If the radius of the wheel is 20cm, find the angular speed of the wheels. Ans. 100 rad/s

* 16. A wooden slab, starting from rest, slides down an inclined plane of length 10m with an acceleration of 5 m/s. What would be its speed at the bottom of the inclined plane?

Hint :

t = 2Sv = 0 + at= 5 2 = 10 m/s

17. A train starting from rest and moving with a uniform acceleration attains a speed of 90 km/h in 5 mm. Find (a) the acceleration and (b) the distance traversed.Hint:u = 0

t = 300 s

a = S = at2

= 3.75km

*18. A person rows his boat in a stream with a speed of 2.0 m/s. Water in the stream is flowing perpendicular to the direction of flow, find graphically his resultant velocity. Ans. 2.5 m/s

19. A bus starting from rest moves with a uniform acceleration of 0.1 m/s2 for 2 mm. Find (a) the speed acquired and (b) the distance travelled.Hint : u = 0a = 0.1 m/s2t = 60 2 sv = at = 12 m/s

S =

*20. A train is travelling at 90 km/h. The brakes are applied so as to produce a uniform acceleration of - 0.5 m/s2. Find how far the train goes before it stops?Hint :a = - 0.5 m/s2

v = 0S = ?

We know, S =

S =

orS = 21. Find the initial velocity of a train which is stopped in 20 s by applying brakes. The retardation due to brakes is 1.5 m/s2.Hint:u = ?t = 20 sv = 0a = - 1.5 m/s2V = u + atO = u - 1.5 20= u - 30u = 30 m/s

*22. A bullet leaves the barrel of a rifle with a speed of 300 m/s. If the length of the barrel is 0.9 m, at what rate is the bullet accelerated while in the barrel?Ans. 5 x 104 m/s2

23. A car travels a certain distance with a speed of 40 ms-1 and returns with a speed u. If the average speed for the whole journey is 48 ms-1, what is the value of u?Ans. 60 ms-1

24. An object of mass 0.5 kg is whirled at the end of a string 0.8 m long. If the string makes three revolutions in 1.2 s, find the tension in the string. Ans. 35.6 N

25. A body starts from rest and is found to cover 3 m during the 5th second of its motion. Find the acceleration if it is uniformly accelerated. Ans. 0.67 m/s2

*26. An aeroplane, taking off from a field, has a run of 500 m. What is the acceleration if it leaves the ground in 10 s from the start? Also find the take off velocity.Ans. 10 m/s2, 100 m/s

27. A train 50 m long passes over a bridge 250 m long at a velocity of 30 km/h. How long will it take to completely pass over the bridge? Ans. 36 s

28. A cyclist goes uphill at a speed of 8 km/h and downhill at a speed of 32 km/h. If the uphill and downhill journeys involve the same distance, what is his average speed during the whole journey. Ans. 12.8 km/h

*29. The figure given below is the distance-time graph of an object. Do you think it represents a real situation? If so, why?Ans. It does not represent a real situation.

30. Look at the graphs (a) to (d) in Fig. 1.21 carefully and state with reasons, which of these cannot possibly represent one dimensional motion of a particle. Hint:(a) it is not possible. A line drawn parallel to position-axis will cut the graph at P and Q corresponding to x1 and x2 for the same time, which is absurd.(b) It is not possible. Similarly, for the same time the particle cannot have two velocities v1and v2. (c) It is not possible because the speed can never be negative.(d) It is not possible as the total path length travelled by the particle cannot decrease withtime.

*31. Represent graphically the motion of a body starting from rest and moving with uniform acceleration both in terms of velocity-time and displacement-time axes.

Hint:

*32. The position-time (x t) graphs for two children A and B returning from their school 0 to their homes P and Q respectively are shown in Fig. 1.24. Choose the correct entries in the brackets below:(i) (A/B) lives closer to the school than (B/A).(ii) (A/B) starts from the school earlier than (B/A).(iii) A and B reach home at the (same/different) time.(iv) (A/B) overtakes (B/A) on the road (once/twice).(v) (A/B) walks faster than (B/A). Hint:(i) A lives closer to the school than B because P is close to 0 then Q.(ii) A starts from the school earlier than B because A starts when t = 0.(iii) A and B reach homes at different times (A reaches after t1 and B after t9).(iv) As the two curves intersect at one point only, B overtakes A on the road once.(v) Since the curve for B is steeper than for A, B walks faster than A.

33. Do the following two graphs represent same types of motion? Name the motion. Ans. Both the graphs represent non-uniform motion34. In case of uniform linear motion, what is the value of acceleration?Ans. Zero

*35 Separate the vector and scalar quantities from the following: distance, velocity, displacement, speed.Ans. distance and speed are scalar quantities

36. A body starts from rest, and moves along a straight line. It has uniformly accelerated motion upto time t1. During the interval t2 - t1, it moves with uniform velocity. After time t2 its motion is retarded, and it comes to rest at time t3. Draw the velocity-time graph.Hint: Refer to Fig. 1.26.

37. Mohen takes 15 minutes to go from his home to school and 30 minutes for the return journey. If the distance between the school and the home is 4.5 km, what is his average velocity?

Hint:

*38. Read each statement below carefully, and state with reasons and examples if it is true or false. A particle in one-dimensional motion(a) with zero speed at an instant may have non-zero acceleration at that instant.(b) with zero speed may have non-zero velocity.(c) with constant speed must have zero acceleration.(d) with positive value of acceleration must be speeding up.

Hint:(A) True (B) False (C) True (D) False

39. A car accelerates from rest at a constant rate A for sometime, after which it retards at a constant rate B to come to rest. If the total time lapse is T seconds, evaluate the maximum velocity reached and the total distance travelled in terms of A, B and T.Hint:Let us plot the given statement graphically.Let t1 + t2 = T

is the maximum velocity

Ort1+t2 = T =

Or

Total distance travelled = Area under the v t graph = Area of AMN

The required distance =

*40. A train starts from a station P with a uniform acceleration a1 for some distance and then goes with the uniform retardation a2 for some more distance to come to rest at the station Q. The distance between the stations P and Q is 4 km and the train takes 4 minutes to complete this journey. If the accelerations are in km per minute2 unit,

show that, SolutionSuppose the train moves from P to R with uniform acceleration a1 and then from R to Q with retardation a2.Taking PR = S1 and RQ = S2 and t1, t2 be the times taken for these two parts respectively, we can write,S1 + S2 = 4 kmt1 + t2 = 4 minFor the part PR, we can write

S1 = (i)For the part RQ we can write

(ii)From (i) and (ii) we have,

OrOrV = 2 km/minAlso,v = 0 + a1t1 and 0 = v - a2t2

Ort1 =

Thus,, which is the required relation.

*41. The speed of a train increases at a constant rate a from zero to v, and then remains constant for an interval, and finally decreases to zero at a constant rate /3. If L be the total distance described, prove that the total time taken is

.Sol.The given problem can be graphically represented as shown below.

The distance (L) travelled by the train is equal to the area under the v - t graph on the time on the time-axis.

L = Area of OPM + Area MPQN + Area of NQR

=

Or

= + t2Total time taken = (t1 + t3) + t2

=

= [From (i)]

42. A body travels 2 m in the. 2nd second and 6 m in the next four seconds. What will be the distance travelled in the 9dI second? Ans. 12 cm

*43.A body travels 10 m in first three seconds and 15 m in the next four seconds. What is the velocity at the end of 8th second? Ans. 2.54 mc1

44. A body starts from rest and is uniformly accelerated. It travels a distance x in t s. Show that the distance travelled in the tth second of its motion is

OBJECTIVE EVALUATION

I TRUE OR FALSE STATEMENTS

State whether the following statements are True (T) or False (F).

1.The distance travelled by a body starting from rest and moving with uniform acceleration is directly proportional to the square of the time.

2. Motion of an object moving in a circle with constant speed is an example of accelerated motion.

*3.The graph between velocity and time for uniform acceleration is a curved line.

4. If acceleration is zero, the velocity is also zero.

5. Speed can be uniform even if velocity is not uniform.

6. SI unit of angular velocity is rad/s.

7. When a body starts moving from rest its initial velocity is zero.

*8. A body moves from P and Q with a certain velocity and returns from Q and P with the same velocity. Its average velocity during the whole journey is zero.

9. Speed is a fundamental physical quantity.

10. SI unit for velocity is m/s.

11. SI unit for retardation is m/s2.

12. Vector quantities are those which are completely described by magnitude alone.

*13. Whenever a moving body is brought to rest its acceleration is always zero.

14. If a body goes from a certain point and comes back to the same point; its displacement is zero.

15. Average speed =

16. The velocity of a body moving in a circle remains constant.

* 17. The distance travelled by a body, moving with uniform acceleration, is proportional to time.

18. The change of position of an object is called distance.

19. The units of speed and velocity are different.

20. Negative acceleration is called retardation.\

Answers1. T 2. T 3. F 4. F 5. T 6. T7. T 8. F9. F 10. T 11. T 12. F13. F 14. T 15. T 16. F 17. F 18. F19.F 20.T

II FILL IN THE BLANKS

Fill in the blanks using suitable word(s):

1.Linear velocity = __________ x radius of the circle.

2. SI unit of angular velocity is __________ .

3. Displacement is a quantity. -

*4 Energy is a quantity.

5. Force is a physical quantity having magnitude and __________

6. A train is moving out of a railway station. Then the platform is at/in with respect to the train.

7. Distance travelled is always

*8. If the distance-time graph is a straight line, then the body has a __________ motion.

9. If the distance-time graph is curve, then the body has a _________- motion.

*10.Speed and velocity are expressed in __________ units.

11. Velocity of a body is its speed in a particular

12. The velocity of a body at any particular instant during its motion is called velocity.

13. When the velocity of a body decreases with time, its acceleration is __________

14. The uniform acceleration is also called __________ acceleration.

*15. If the acceleration of a body is 8.5 ms2, then its retardation is _________

16. A body falling freely under gravity has uniform __________

17. The velocity-time graph of a body having uniform acceleration is a __________

*18. When a body travels with uniform velocity, its acceleration is __________

19. The slope of distance against time is __________

20.One radian is equal to degrees.

Answers1. Angular velocity 2. rad s-1 3. quantity 4. scalar5. direction 6. motion 7. positivc 8. uniform9. non-uniform 10. same 11. direction 12. instantaneous13. negative 14. constant 15. 8.5 ms2 16. acceleration17. straight line 18. zero 19. speed 20. 57.3

III MATCH THE ITEMSMatch the items of Column A with the corresponding items of Column B.Column A Column B

(i) speed (a) radian per second(ii) displacement (b) radian(iii) retardation (c) metre(iv) angular velocity (d) metre per second(v) angular displacement (e) metre per (second)2

Answers(i) (d) (ii) (c) (iii) (e) (iv) (a) (v) (b)

IVMULTIPLE CHOICE QUESTIONS

Tick () the only correct choice amongst the following:

1.Unit of acceleration is(A) m/s (B) ms (C) m/s2 (D) none of these

2. A body goes ft m A to B with a velocity of 20 m/s and comes back from B to A with a velocity of 30 m/s. The average velocity of the body during the whole journey is(A) zero (B) 24 M/s (C) 25 m/s (D) none of these

3. A body covers half the distance with a speed of 20 m/s and the other half with a speed of 30 m/s The average velocity of the body during the whole journey is(A) zero (B) 24 m/s (C) 25 m/s (D) none of these

*4. In the equation of motion, S = ut = 1/2 at2, S stands for(A) distance in t seconds (B) maximum height reached (C) distance in the tth second(D) none of these

5. Choose the wrong statement:(A) Retardation is a vector quantity.(B) Acceleration due to gravity is a vector quantity.(C) Average speed is a vector quantity.(D) Displacement is a vector quantity.

6. In the equation of motion, x = at + bt2, the units of a and b respectively are(A) m/s2, m/s (B) m/s, m/s2 (C) m/s, m/s (D) none of these

7. A body is thrown up with an initial velocity u and covers a maximum height of h, then h is equal to

(A) (B) (C) 2 ug(D) none of these*8. The seconds hand of a watch is 2 cm long. The speed of the tip of this hand is(A) 0.21 cm/s (B) 2.1 cm/s (C) 21.0 cm/s (D) none of these

9. A body is thrown vertically upwards and rises to a height of 10 m. The velocity with which the body was thrown upwards is (g = 9.8 m/s2).(A) 10 m/s (B) 20 m/s (C) 14m/s (D) none of these

10. In problem no. 9, the time taken by the body to reach the highest point is(A) 1.43s (B) 4.1s (C) 1.24s (D) none of these

11. If the time-displacement graph of a particle is parallel to the time-axis, the velocity of the particle is(A) infinity (B) unity (C) equal to acceleration of the body(D) zero

* 12. Velocity-time graph AB (Fig. 1.29) shows that the body has(A) a uniform acceleration(B) a uniform retardation(C) uniform speed(D) initial velocity OA and is moving with uniform retardation13. Velocity-time graph AB (Fig. 1.30) shows that the body has(A) uniform acceleration(B) uniform retardation(C) uniform velocity throughout its motion and has zero initial velocity(D) none of these* 14. The distance travelled by a freely falling body is propor tional to(A) the mass of the body(B) the square of the acceleration due to gravity(C) the square of the time of fall(D) the time of fall

15. The rate of change of displacement with time is(A) speed (B) acceleration (C) retardation (D) velocity

16. A body strikes the floor vertically with a velocity u and rebounds at the same speed. The change in velocity would be(A) u (B) 2u (C) 3u (D) zero

*17. The moon is 4 x 108 m from the earth. A radar signal transmitted from the earth will reach the moon in about(A) 5.2s (B) 1.3s (C) 2.6s (D) 0.70s

18. A and B are arguing about uniform acceleration. A states that acceleration means the longer you go. B states that acceleration means the further you go. who is right?(A) A (B) B (C) both (D) none

*19. A particle experiences constant acceleration for 20 s after starting from rest. If it travels a distance X1, in the first 10s and distance X2, in the remaining 10s, then which of the following is true?(A) X1 = 2X2 (B) X1 = X2 (C) X1 = 3X2 (D) none of these

20. If a trolley starts from rest with an acceleration of 2 mIs2, the velocity of the body after 4s would be(A) 2 m/s (B) 8 m/s (C) 4 m/s (D) 6 m/s

21. A train passes over a 400 m long bridge. If the speed of the train is 30 m/s and the train takes 20 s to cross the bridge, find the length of the train.(A) 400 M (B) 600 M (C) 800 M (D) 200 M

22. The SI unit for the average velocity is(A) M/s (B) km/s (C) cm/s (D) mm/s

*23. The SI unit for the resultant velocity is(A) m/s (B) km/s (C) cm/s (D) mm/s

24. A train 50 m long passes over a bridge at a velocity of 30 km/h. If it takes 36 s to cross the bridge, the length the length of the bridge will be(A) 100 m (B) 200 m (C) 250 m (D) 300 m

*25. The SI unit for angular velocity is(A) m/s (B) rad (C) rad/s (D) m/rad

26. N kg-1 is NOT the unit of(A) retardation (B) acceleration (C) rate of change of velocity(D) all the above

27. A ball is thrown up with a certain velocity. It attains a height of 40 m and comes back to the thrower. Then the(A) total distance covered by it is 40 m(B) total displacement covered by it is 80 m(C) total displacement is zero(D) total distance covered by it is zero

28. The acceleration of a body projected upwards with a certain velocity is(A) 9.8 m/s2 (B) - 9.8m/s2 (C) zero (D) insufficient data

29. A driver is driving his car along a road is shown in Fig. 1.31. The driver makes sure that the speedometer reads exactly 40 km/h. What happens to the speed of the car from P to Q?

(A) speed remains constant(B) speed first increases then decreases (C) speed first decreases then increases (D) nothing can be decided

30. In the above question, what happens to the velocity of the car from P to Q?(A) velocity remains constant(B) velocity first increases then decreases(C) velocity first decreases then increases(D) nothing can be decided

31. In Question 29, the driver should say that(A) the average speed is 40 km/h (B) the average velocity is 40 km/h (C) the average speed is 80 km/h (D) the average velocity is 80 km/h

*32. A stone tied to a string is whirled in a circle. As it is revolving, the rope suddenly breaks. Then(A) the stone files off tangentially(B) the stone moves radially inward(C) the stone moves radially outward(D) the motion of the stone depends upon its velocity

33. In the following graph (Fig. 1.32) of displacement versus time,(A) the body is at rest(B) the body has some initial speed(C) the body moves with constant speed(D) the body moves with constant velocity

*34 Figure 1.33 shows the displacement-time graphs (a) and (b) for a body moving in a straight path drawn on the same scales. Then(A) slope of line in (a) is greater than the slope of line in (b)(B) slope of line in (b) is greater than the slope of line in (a)(C) slope of line in (a) is equal to the slope of line in (b)(D) nothing can be said about the slopes

35. It follows from Question 34, that the velocity in case of (b) is(A) more than the velocity in case of (a)(B) less than the velocity in case of (a)(C) equal to the velocity in case of (a)(D) square of the velocity in case of (a)

36.In Fig. 1.34, BC represents a body moving(A) backward with uniform velocity(B) forward with uniform velocity(C) backward with non-uniform velocity(D) forward with non-uniform velocity

37. In Fig. 1.35, the velocity of the body at A is(A) zero (B) unity(C) maximum (D) infinite

38. In the above question, the velocity(A) increases between point 0 and A (B) increases between point A and B (C) decreases between points A and B(D) is zero throughout

39. A body moving along a circular path has(A) a constant speed(B) a constant velocity(C) no tangential velocity(D) no radial acceleration

40. In Fig. 1.36(A) retardation is uniform(B) velocity is decreasing with time(C) beyond M, the body has negative velocity(D) all the above are correct

41. P is moving in a straight line with uniform velocity. Q is moving in a straight line with steadily increasingvelocity.

Which of the following (Fig. 1.38) shows, Qs apparent path w.r.t P?(A) A (B) B (C) C (D) D*42.The velocity of a particle increases from u to v in a time t during which it covers a distance S. If the particle has a uniform acceleration, which one of the following equation does not apply to the motion?

(A) 2 S = (v +u) t(B) (C) v2 = u2 2 aS(D) 43. Which of the following (Fig.1.40) would probably show the velocity-time graph for a body whose acceleration-time graph is shown in Fig. 1.39?

44. The velocity-time graph of a body falling from rest under gravity and rebounding from a solid surface is represented by which of the graphs shown in Fig. 1.41?

*45 The unit for the rate of change of velocity will be(A) m/s (b) m/s2 (C) Ns (d) N/s

46. The acceleration-time graph for a body is shown in Fig. 1.42. The most probable velocity-time graph for the body is

47. A cyclist moves from a certain point X and goes round a circle of radius r and reaches Y, exactly at the other side of the point X, as shown in Fig. 1.44. The displacement of the cyclist would be

(A) (B) (C) (D)

48. In the above problem, the distance covered by the cyclist would be

(A) (B) (C) 2r (d)

49. Which of the following relation represents the relationship between the average speed, time and distance correctly?(A) Average speed = distance x time

(B) Average speed = (C) Time = average speed + distance(D) Distance = average speed (time)2

*50. When a graph between two physical quantities is a straight line, the two quantities are:(A) both constant(Bb) independent(C) directly proportional(D) inversely proportional

51. A body moving along a circular path, has(A) constant speed(B) constant velocity(C) no radial acceleration(D) no tangential velocity

*52. Area under a velocity-time graph gives(A) the time taken by a moving object(B) the distance travelled by a moving object(C) the acceleration of moving object(D) the retardation of a moving object

53. When the distance an object travels is directly proportional to the length of time, it is said to travel with(A) constant speed (B) zero velocity (C) constant acceleration(D) uniform velocity

54. Which of the following physical quantity is different from others?(A) speed (B) distance (C) energy (D) average velocity

55. Which of the following physical quantity is different from others?(A) displacement (B) velocity (C) force (D) kinetic energy

*56. The speed of a body describing its motion is(A) direction (B) state (C) type (D) rapidity

57. Which of the following distance-time graph (Fig. 1.45) represents the accelerated motion of a body?

58. A body moves along the circumference of a circular track of radius R (Fig. 1.46). What is displacement of the body when it covers 3/4th of its circumference?

(A) 3R(B) (C) (D)

59. Which of the following represents distance (S) - time (t) graph (Fig. 1.47) for a retarded motion?

60. A rubber ball dropped from a certain height is an example of(A) uniform acceleration. (B) uniform retardation (C) uniform speed (D) non - uniform speed

*61. If the velocity of a body does not change, its acceleration is(A) zero (B) infinite (C) unity (D) none of these

62. The velocity-time graph for a body with non-uniform motion is a(A) straight line (B) straight line parallel to x-axis (C) straight line parallel to y-axis(D) curved line

*63. The ratio of SI units to CGS units of retardation is(A) 10-2 (B) 102 (C) 10 (D) 10-1

*64. The physical quantity corresponding to the rate of change of displacement is(A) speed (B) velocity (C) acceleration (D) retardation

65. The velocity of a body at rest is always(A) unity (B) negative (C) zero (D) infinite

66. When the distance an object travels is directly proportional to the length of time, it is said to travel with(A) zero velocity (B) constant speed (C) constant acceleration(D) uniform velocity

67. In the following speed-time graph, the shaded portion gives(A) distance travelled (B) average speed (C) average velocity(D) displacement travelled

68. A car increases its speed from 20 km/h to 50 km/h in 10 seconds. Its acceleration is(A) 30 ms-2 (B) 3 ms-2 (C) 18 ms-2 (D) none of these

*69. A body whose speed in a particular direction is constant(A) must be accelerated (B) might be accelerated (C) has a constant velocity(D) cannot be accelerated

*70. A body has an acceleration of - 4 ms-2. What is its retardation?(A) - 4ms2 (B) 4 ms-2 (C) zero(D) nothing can be decided

*69. A body whose speed in a particular direction is constant(A) must be accelerated (B) might be accelerated (C) has a constant velocity (D) cannot be accelerated

*70. A body has an acceleration of -4 ms-2. What is its retardation?(A) - 4ms2 (B) 4 ms-2 (C) zero(D) nothing can be decided

FORCE AND NEWTON'S LAWS

UNSOLVED NUMBERICAL PROBLEMS

1. How much force is needed to accelerate a trolley of mass 20 g through 1 m/s2?Ans. 2 x 10-2 N

2. A force of 100 N acts on a mass of 25 kg for 5 s. What velocity does it generate ?Ans. 20 M/s

3. A bullet leaves a rifle with a velocity of 100 m/s and the rifle (mass = 2.5 kg) recoils with a velocity of 1 m/s. Find the mass of the bullet. Ans. 0.25 kg

4. A certain force acting on a mass of 15 kg for 3 s, gives it a velocity of 2 m/s. Find the magnitude of the force. Ans. 10 N

*5 A cricket ball of mass 0.15 kg is moving with a velocity of 1.2 m/s. Find the impulse on the ball and the average force applied by the player if he is able to stop the ball in 0.18s. Ans.0.l8Ns, 1 N s

6. A motor car of mass 2000 kg is moving with a certain velocity. It is brought to rest by the application of brakes, within a distance of 20 m when the averag resistance being offered to it is 5000 N. What was the velocity of the motor car?Ans. 10 m/s

7. A body of mass 0.5 kg undergoes a change in velocity of 4 cm/s in 4 s. What is the force acting on it? Ans. 5 x 10-3 N

8. A force of 8 N acting on an 8 kg mass for 4 s provides it some velocity. Calculate the velocity. Ans. 4 m/s

9. What would be the weight of a body of mass 50 kg on the surface of the moon, where g = 1.6 m/s2? What would be its mass? Ans. 80 N, 50 kg

*10. A boy jumps a distance of 2 m on the surface of the earth. What distance will he jump on the surface of the moon, where g is of its value on the surface of the earth? Ans. 12 m

11. Two bodies of mass 1 kg and 2 kg respectively moving in the directions opposite to each other with a speed 5 m/s collide. Calculate the total momentum of the system before collision. Ans.- 4 kg m/s

12. A bullet of mass 15 g leaves the barrel of a gun with a velocity of 120 m/s. The gun recoils with a velocity of 1 m/s. The gun recoils with a velocity of 1 m/s. Find the mass of the gun. Ans. 1.8 kg

13. A force of 3 N acts on a mass of 0.5 kg at rest for 10 s. Find the final velocity and the momentum of the body after 10 s. Ans. 60 m/s, 30 kg m/s

* 14. A force of 80 N acting on a certain mass for 3.0 s gives it a velocity of 6.0 m/s. Find the mass of the body if the body was initially at rest. Ans. 40 kg

15. A toy of mass 0.1 kg acquires a speed of 5.0 m/s when pushed forward. What is theimpulse given to the toy? Ans.5.0 N

16. A projectile weighing 200 kg is fired from a gun with a velocity of 500 m/s. If the velocity of recoil of the gun is 12.5 m/s, calculate the mass of the gun.Ans. 8000 kg

17. A car of mass 2500 kg accelerates at the rate of 4.0 m/s2 and then at the rate of 16 m/s2. Calculate the ratio of the forces exerted by the engine in the two cases.Ans. 1/4

*18. Two masses 7 kg and 12 kg are connected at the two ends of a light inextensible string that passes over a frictionless pulley as shown in Fig. 2.11. Find the acceleration of the masses and the tension in the string when the masses are released.Ans. 2.58 ms2, 86.6 N

19. A 10g bullet is shot from a 10 kg gun with a velocity of 400 ms* What is the velocity of recoil of the gun?Ans.- 0.4 ms

*20 A hunter has a machine gun that can fire 50 g bullets with a velocity of 75 ms* A 60 kg tiger springs at him with a velocity of 10 ms1. How many bullets must the hunter fire per second into the tiger in order to stop him in his track?Ans. 160

21. A shall of mass 0.02 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80ms, what is the recoil speed of the gun?Ans. - 0.016 ms-1

22. A rocket with a lift off mass 20000 kg is blasted upwards with a net acceleration of 5 ms-2. Calculate the initial thrust of the blast.Ans. 2.96 x 105 N


I TRUE OR FALSE STATEMENTS

State whether the following statements are True (T) or False (F):

1. Force may or may not produce any motion in a body.

2. Action and reaction act on the same body.

3. 1N = 1kg x m/s2

4. The SI unit for impulse is kg m/s.

5. Impulse represents the rate of change of momentum of a body.

*6. Momentum is a vector quantity

7. 1 N is that force which produces an acceleration of 1 m/s2 in a body of mass 1 g.

8. In the game of carrom, we use powder to decrease friction.

9. In any interaction there are always at least two forces in play.

10. The force of friction is smaller in solids than in liquids.

11. The first law of motion is also known as Galileos law of inertia.

* 12. A ball thrown upwards in a running train continues to move along the train due to inertia of motion.

13. Balanced forces do not change the speed of the body.

14. Impulse is a scalar quantity.

15. If the resultant of forces is zero, they are said to be balanced.ANSWERSQ.12345678910

Ans.TFTFFTFTTF

Q.1112131415

Ans.TTTFT


Fill in the following blanks with suitable word (s):

1. Dyne is the C.G.S. unit of _________

2. 1 new ton is that force which produces an acceleration of _______ in a body of mass 1 kg.

*3 The passengers in a bus tend to fall ___________ when it starts suddenly.

4. A heavier body has more __________ than a lighter body.

5. The unbalanced forces acting on a body produce in it.

6. The single force which acts on a body to produce the same effect in it as is done by all the forces together is known as ___________ force.

7. A body is said to be under balanced forces when the resultant force acting on the body is __________

*8. Force has __________ and direction.

9. Newtons first law of inertia is also known as Galileos law of __________

10. The SI unit of momentum is _________

11. To every action there is an equal and _________ reaction.

12. Action and reaction always act on __________ bodies.

13. Ns is the SI unit of __________

*14. Friction is a self adjusting

15. Kg wt is the gravitational unit of __________

ANSWERS1. force 2. 1ms-2 3. backward 4. inertia5. motion 6. resultant 7. zero 8. magnitude9. inertia 10. kg ms-1 11. opposite 12. different13. impulse 14. force 15. Force

III MATCH THE ITEMS

Match the items of Column A with the corresponding items of Column B.

Column A Column B

(i) change in momentum (a) m-1(ii) resultant force (b) ms-2(iii) impulse (c) no unit(iv) acceleration (d) N(v) change in velocity (e) N s(vi) inertia (f) kg ins1

Answers(i) (f) (ii) (d) (iii) (c) (iv) (b) (v) (a) (vi) (c)

IV MULTIPLE CHOICE QUESTIONS


1. The product of force and time is called (A) thrust(B) impulse(c) pressure (d) none of these2. Choose the wrong statement:(A) 1kg wt = 9.8N(B) Momentum is awector quantity.(C) Force is always conserved.(D) Momentum is conserved in the absence of an external force.

*3. A long-jumper runs before jumping because(A) he covers a greater distance(B) he maintains momentum conservation(C) he gains energy by running(d) he gains momentum

4. Two unequal masses (m1 and m2) are connected by a string which passes over a frictionless pulley (Fig. 2.12). If m1, m2 and the table are frictionless, the acceleration of the masses would be

(A) (B) (C) (D) None of these

5. The weight of a body would not be zero(A) at the centre of the earth (B) during a free fall (C) in interplanetary space(D) on a frictionless surface

6. An iron ball and a wooden ball of the same radius are released from a height H in vacuum. The time taken by both of them to reach the ground are(A) roughly equal(B) unequal (C) exactly equal(D) in the inverse ratio of the their diameters

7. A man is standing on a boat in still water. If he walks towards the shore the boat will(A) move away from the shore (b) remain stationary (c) move towards the shore(d) sink

*8. During a planned manoeuvre in a space flight, a free-floating astronaut A pushes another free-floating astronaut B, the mass of A being greater than that of B. Then, the magnitude of the force exerted by astronaut A on astronaut B is(A) equal to zero(B) equal to the force exerted by B on A (C) greater than the force exerted by B on A (d) less than the force exerted by B on A

9. In the above problem, during a push(A) the acceleration of A is greater than that of B(B) the acceleration of A is less than that of B(C) neither is accelerated(D) their accelerations are equal in magnitude but opposite in direction

* 10. A bullet of mass A and velocity B is fired into a block of wood of mass C. If loss of any mass and friction be neglected, the velocity of the system must be

(A) (B) (C) (D)

11. A single horizontal force F is applied to a block of mass M, which is in contact with another block of mass M (Fig. 2.13). If the surfaces are frictionless, the force between the blocks is

(A) (B) (C) (D) none of these

* 12.A driver accelerates his car first at the rate of 1.8 m/s2 and then at the rate of 1.2 m/s2. The ratio of the forces exerted by the engines will be respectively equal to(A) 2 : 3 (B) 1: 2 (C) 2 : 1 (D) 3 : 2

13. A body of mass 5 kg undergoes a change in speed from 30 to 40 m/s. Its momentum would increase by(A) 50 kg m/s (B) 75 kg m/s (C) 150 kg m/s (d) 350 kg m/s

14. The force needed to produce an acceleration of 6 m/s2 in a ball of mass 4 kg will be(A) 24 N (B) 30 N (C) 32 N (D) 36 N

15. A body of mass 5 kg undergoes a change in speed from 20 to 0.20 m/s. The momentum of the body would(A) increase by 99 kg m/s (B) decrease by 99 kg m/s (C) increase by 101 kg m/s(D) decrease by 101 kg m/s

*16. A bullet of mass 0.01 kg is fired from a gun weighing 5.0 kg. If the initial speed of the bullet is 250 mis, calculate the speed with which the gun recoils.(A) 0.50 m/s (B) + 0.05 m/s (C) 0.25 m/s(D) + 0.25 m/s

17. A body of mass 100 g is moving with a velocity of 15 rn/s. The momentum associated with the ball will be(A) 1.5 kg m/s2 (B) 1.5 kg m/s (C) 2.5 kg m/s (D) 3.2 N s

18. A number of discs, each of momentum M kg m/s are striking a wall at the rate of n discs per minute. The force associated with these discs, in newton, would be

(A) (B) 60 Mn(C) (D) 20. If action and reaction were to act on the same body,(A) the resultant would not be zero (B) the body would not move at all(C) both (a) and (b) are correct (D) neither (a) nor (b) is correct

*21. A stationary ball weighing 0.25 kg acquires a speed of 10 m/s when hit by a hockey stick. The impulse imparted to the ball is(A) 2.5 N s (B) 2.0 N s (C) 1.5 N s (D) 0.5 N s

22. A stone is tied to the middle of a string and suspended from one end as shown in Fig. 2.14. Here S is the stone and 0 is the point of suspension. If you give a sharp jerk at P, the string will break(A) below the stone (B) at the point P itself(C) from above the stone (D) nothing can be decided

23. In the above problem, if we increase the pull at P gradually, the string will break(A) below the stone(B) at the point P itself(C) from above the stone(D) nothing can be decided

24. The above problem can be explained on the basis of the property of(A) inertia (B) force(C) momentum (D) torque

*25. The combined effect of mass and velocity is taken into account by a physical quantity called(A) torque(B) moment of force(C) momentum(D) moment of momentum

26. Momentum is a measure of(A) weight (B) mass (C) quantity of motion(D) velocity

27. Momentum has the same units as that of(A) impulse (B) torque (C) moment of momentum (d) couple

*28. Consider two spring balances hooked as shown in Fig. 2.15. We pull them in opposite directions. If the reading shown by A is 1.5 N, the reading shown by B will be(A) 1.5 N (B) 2.5 N (C) 3.0 N (D) zero

29. A hammer weighing 3 kg, moving with a velocity of 10 m/s, strikes against the head of a spike and drives it into a block of wood. If the hammer comes to rest in 0.025 s, the impulse associated with the ball will be(A) 30 N s (B) 30 N s (C) 15 N s (D) 15 N s

30. In the above problem, the average retarding force acting on the spike will be(A) 600 N (B) 600 N (C) 1200 N (D) 1200 N

31. In a tug-of-war between the teams A and B, the rope breaks at a point which is nearer to A. Then(A) A has applied more force(B) B has applied more force(C) A and B both have applied same force (D) none has applied any force

*32.A rocket works on the(A) first law of motion(B) third law of motion(B) second law of motion(D) law of conservation of energy

33. A metallic ball strikes a wall and falls down whereas a tennis ball having the same mass and velocity bounces back. The reason for this is that(A) both suffer equal change in momentum (B) the tennis ball suffers a greater change in momentum (C) metallic ball suffers a grater change in momentum(D) the momentum of the tennis ball is less than that of the metallic ball.

*34. Kg ms-1 is same as(A) N(B) NS(C) NS-2(D) Ns-3

35. If you are asked to push an object so that the acceleration produced in it is now twice as before, then the force required will be(A) twice as before (B) half as before(C) same as before (D) four times as before

36. It is difficult to walk on ice because of(A) absence of friction (B) absence of inertia (C) more inertia(D) more friction

37. The law which defines force is(A) Newtons third law of motion(B) Newtons first law of motion(C) Newtons second law of motion(D) Newtons law of gravitation

38. The law which gives a quantitative(A) Newtons third law of motion(B) Newtons first law of motion(C) Newtons first law of motion(D) Newtons law of gravitation measurement of force is

39. Internal forces(A) are always balanced forces (B) never balanced forces(C) (c) may or may not be balanced (D) none of these

*40. External forces(A) are always balanced (B) never balanced(C) may or may not be balanced (D) none of these

*41. The ratio of SI unit to CGS unit of force is(A) 10-5(B) 103(C) 10-3 (D) 105

42. A and B are two objects with mass 6 kg and 34 kg respectively.(A) A has more inertia than B (B) B has more inertia than A (C) A and B both have same inertia(D) none of the above is true

43. Which of the following class of force is different from others?(A) pulling of a cart (B) stretching of a coiled spring (C) kicking of a football(D) electrical force

*44.Which of the following class of force is different from others?(A) magnetic force (B) electrical force (C) gravitational force(D) stretching of a spring

45. A body is said to be unier balanced forces when th resultant force acting on the body is(A) unity (B) zero (C) infinite (D) none of these

*46.P and Q are two object with masses 5 kg and 30 kg respectively. Then(A) P has more inertia than Q (B) Q has more inertia than P (C) P and Q have the same inertia(D) neither P nor Q has any inertia.

47. The ratio of SI unit to CGS unit of momentum is(A) 103 (B) 105 (C) 10-5 (D) 102

48. Which of the following represents the SI unit of force?(A) dyne (B) gram-weight (C) newton (D) kilogram-weight

49. 1 dyne is equal to

(A) 981 g wt (B) (C) 981 kg wt (D) none of these

*50. When an object undergoes acceleration(A) its speed always increases (B) its velocity always increases(C) it always falls towards the earth (D) a force always acts on it

51. A force acts on an object which is free to move. If we know the magnitude of the force and the mass of the object, newtons 2nd law of motion enables us to determine the objects(A) weight (B) speed (C) acceleration (D) position

52. When a force of 1 newton acts on a mass of 1 kg that is able to move freely, the object moves with an(A) speed of 1ms-1 (B) acceleration of 1 ms-2 (C) speed of 1 kms-1 (D) accelerations of 10 ms-2

*53. When a net force acts on an object, the object will be accelerated in the direction of the force with an acceleration proportional to the(A) force on the object (B) velocity of the object (C) mass of the object(D) inertia of the object

*54. Newton used the phrase quantity of motion for(A) momentum (B) force (C) acceleration due to gravity(D) none of these

55. The effect of an impulse force on the body is measured only in terms of its(A) force (B) moment of momentum(C) impulse(D) none of these

56. kg ms-1 is the SI unit of(A) impulse(B) force(C) angular velocity (D) none of these

*57. The gravitational unit of force in the metric system is(A) g wt (B) N (C) kg wt(D) none of these

*58. Galileos law of inertia is another name for newtons law of motion.(A) first (B) second (C) third(D) any one of the above

59. Frictional force cant be measured in(A) kg wt (B) newton (C) dyne (D) kg ms-160. Time rate of change of linear momentum is called(A) pressure (B) impulse (C) force(D) none of these

61. Friction is a/an(A) self-adjusting force (B) necessary evil (C) important force in daily life(D) all the above are wrong

62. Three equal weights of mass 2 kg each are hanging on a string passing over a fixed pulley as shown in the figure 2.16. The tension in the string connecting the weights B and C is about(A) zero (B) 13N (C) 3.3 N(D) 19.6 N

63. Two skaters A and B of mass 50 kg and 70 kg respectively stand facing each other 6 metres apart. They then pull on a light rope stretched between them. How far has each moved when they meet?(A) Both have moved 3 metres(B) A moves 2.5 metres and B moves 3.5 metres(C) A moves 3.5 metres and B moves 2.5 metres(D) A moves 2 metres and B moves 4 metres

*64. A cannon after firing recoils due to(A) conservation of energy(B) backward thrust of gases produced(C) Newtons 1st law of motion(D) Newtons 3rd law of motion

*65. A man of weight W is standing on a lift which is moving upward with an accelerationa. The apparent weight of the man is

(A) (B) W(C) (D) 66. You are marooned on a frictionless horizontal surface and cannot exert any horizontal force by pushing against the surface. How can you get off?(A) by jumping (B) by spitting or sneezing (C) by rolling you body on the surface(D) by running on the plane

67. A body of mass M collides against a wall with velocity V and rebounds with the same speed. Its change in momentum is(A) zero (B) MV (C) -2 MV (D) MV

*68. A machine gun fires n bullets per second and the mass of each bullet is m. If the speed of bullets is v, then the force exerted on the machine gun is

(A) mng (B) mnv (C) mnvg(D) 69. A bullet in motion hits and gets embedded in a solid resting on a frictionless table. What is conserved?(A) momentum and kinetic energy(B) momentum alone(C) kinetic energy alone(D) neither momentum nor kinetic energy

*70. A diwali rocket is ejecting 0.05 kg of gases per second at a velocity of 400 ms-1. The accelerating force on the rocket is(A) 20 dynes (B) 20 newton (C) 20 kg wt(D) sufficient data not given

71. A man sitting in a train in motion is facing the engine. He losses a coin up, the coin falls behind him. The train is moving(A) forward with uniform speed (B) backward with uniform speed(C) forward with acceleration (D) forward with deceleration

72. A monkey is at rest on a weightless rope which goes over a pulley and is tied to a bunch of bananas at the other end. The weight of the bunch of bananas is exactly the same as that of the monkey. The pulley is frictionless and weightless. The monkey starts to climb up the rope to reach the bananas. As he climbs, the distance between him and the bananas will (A) decrease (B) increase(C) first decrease and then increase(D) remain unchanged

*73. A stretching force of 100 N is applied at one end of a spring balance and an equal stretching force is applied at the other end at the same time. The reading on the balance will be (A) 200 N (B) 100 N (C) 400 N (D) zero

74. The masses of 10 kg and 20 kg respectively are connected by a massless spring. A force of 200 N acts on the 200 kg mass. At the instant shown, the 10 kg mass has an acceleration of 12 ms2, what is the acceleration of 20 kg mass?(A) 12 ms-2 (B) 4 ms-2 (C) 10 ms-2 (D) zero

*75 Physical independence of force is a consequence of(A) First law of motion (B) Second law of motion(C) Third law of motion (D) All of these lawsAnswers Q.12345678910

Ans.B CDADCABBA

Q.11121314151617181920

Ans.CDAABBBAAB

Q.21222324252627282930

Ans.AACACCAABD

Q.31323334353637383940

Ans.ACBBAABCAA

Q.41424344454647484950

Ans.DBDDBBBCBB

Q.51525354555657585960

Ans.CBAACACADC

Q.61626364656667686970

Ans.A, B, CBCDABCBBB

Q.7172737475

Ans.CDBBA

GRAVITATION


1. The value of the force of gravity on a boy of mass 40 kg was found to be 2400 N.Using Me = 6 x 1024 kg and Re = 6.4 x106 m, find the value of G.Ans. 6.67 x 1011 Nm2/kg2

2. Compute the force of gravity on a body of mass 80 kg lying on the surface of the earth. Given mass of the earth 6 x kg, radius of the earth C.4 x 106 m andG = 6.67 x 1011 Nm2/kg2. Ans. g = 9.77 m/s2, 781.6 N

3. Calculate the value of acceleration due to gravity on the surface of the moon (mass of moon = 7.4 x 1022 kg, radius of moon = 1740 km, G = 6.673 x 10-11 Nm2/kg2Ans. 1.63 m2/s

4. Calculate the mass of the earth. Given g = 9.8 m/s2 , Re = 6370 km and G = 6.67 10-11 Nm2/kg2.Ans.5.961024 kg

*5.If gmoon/gearth = 1/6, what height will a man of 60 kg jump safely on the moon, if he jumps 1.5 m on the earth.Ans.9 m

6.A force 20 N acts on a body whose mass is 9.8 kg. What is its acceleration?Ans.2.04 m/s2

7.A force of 2 kg wt acts on a body of mass 4.9 kg. Calculate the acceleration. (g = 9.8 m/s)Ans.4.0 m/s2

8.A ball dropped from a balloon at rest clears a tower 81 m high during the last body when it reaches the ground.Ans.2684.2 m, 324.38 m/s

9.A ball is dropped from a height of 1 m. How long does it take for the ball to reach the ground? With what speed does it hit the ground?Ans.0.45 s, 4.4 m/s

10.Calculate the vertical distance through which the moon falls in 2 days.Ans.40642 km

11.The earths gravitational force causes an acceleration of 5.5 m/s2 in a 2 kg mass somewhere in space. How much would the acceleration of a 3 kg mass be at the same place?

12.What is the vertical distance travelled by a projectile in time t when thrown parallel to the ground? Does it depend upon the speed with which the object is thrown?

Ans., no

13.The value of G is 6.67 10-11 Nm2 kg -2 write down its value in CGS units.Ans.6.67 10-8 dyne cm2 g-2

14.What do you mean by apparent weight? What is the apparent weight of a body during free fall?Ans.Zero

15.What is the mass of an object whose weight is 98 N?Ans.10 kg

16.A ball is dropped from a height of 1 m from the earths surface. How much time would it take to reach the ground? With what speed does it hit the ground?Ans.0.45s, 4.4 ms-1

17.The value of g on the moon is 1.62 ms-2 . If G = 6.67 10-11 Nm2 kg-2 and radius of the moon is 1.74 106 m, what is the mass of the moon? Ans.7.35 1022 kg

18.What is the distance between two bodies each of mass 2kg so that the gravitational force between them is 1 N? Use the standard data.Ans.1.63 10-5 m

19.The gravitational force between two objects is 4 N. What will be the force between them if the distance between them gets doubled?Ans.1 N

20.Use the standard given data to prove that

Given: G = 6.67 10-11 SI unitsMmoon 7.4 1022 kgRmoon = 1.75 106 m

21.What is the value of g on the surface of the sun?Mass of the sun = 1.99 1030 kgRadius of the sun = 6.96 108 m

22.A body is taken to a height Re above the surface of the earth, where Re is radius of the earth. What is the value of acceleration due to gravity at Re?Ans.2.45 ms-2


1.TRUE OR FALSE STATEMENTS

State whether the following statements are True (T) or False (F):

1. Acceleration due to gravity depends upon the mass of body.

2. Mass is measured by spring balance.

3. Projectile is a body which moves in space without any fuel or propulsion.

4. G and g are same.

*5 Weight of body is given by, W = m xg.

6.Bodies falling freely under gravity have no weight.

7. The value of C depends upon the mass of two objects.

8. If a spring balance, holding a heavy object is released, it will read zero weight.

9. The value of C is high if the radius of the body is more and less if radius is less.

*10. The gravitational force between two bodies changes if a material body is placed between them.

11. The acceleration of a body thrown up is numerically the same as the acceleration of a downward falling body but opposite in sign.

12. The value of g is zero at the centre of the earth.

*13. All objects attract each other along the line joining their centre of mass.

14. The atmosphere is not separated from the surface of the earth due to Coulombian force of attraction.

15. Acceleration due to gravity, g = , where symbols have their usual meanings.

Answer

Q.12345678910

Ans.FFTFTTFTFT

Q1112131415

Ans.TTTFT


Fill in the following blanks using suitable word(s):

1. Weight is a _____________ quantity.

2. 1 kg wt = _________________ N.

*3 The weight of a body is the __________ with which it is attracted towards the earth.

4. A body would weigh___________ at the top of a mountain than at its base.

5. The weight of a body becomes __________ at the centre of the earth.

6. The value of g on earth is __________ at the poles and __________ at the equator.

7. Nm2 kg-2 is the SI unit of _________

*8. Gravitational force is an __________ force.

9. When the distance between particles is halved, the gravitational force becomes_________ the two.

10.The law of gravitation was given by_________

11.Weight is measured by a __________ balance.

12.The gravitational force which acts on a mass of 1 kg is ________

13.If the weight of an object is 49 N, its mass is ___________

14.The apparent weight of a body during free fall is __________

15.The horizontal distance travelled by a projectile is called its ___________

Answer(1) Vector(2) 9.8(3) Force(4) Less(5) Zero(6) Maximum(7) G or gravitational constant(8) action - at - a distance(9) Four times(10) Newton(11) spring(12) 9.8 N(13) 5 kg(14) Zero(15) Range

III MATCH THE ITEMS

Match the terms of Column A with the corresponding items of Column B Column AColumn B(i) Gravitational intensity(a) kg(ii) Gravitational force(b) no unit(iii) Gravitational constant(c) n kg-1 (iv) Gravitational field(d) N(v) Gravitational mass(e) Nm2 kg-2

Answers(i) (c)(ii) (d)(iii) (e) (iv) (b) (v) (a)

IV MULTIPLE CHOICE QUESTIONS


1. The universal law of gravitation was postulated by(A) Copernicus (B) Newton (C) Galileo (D) Archimedes

2. A rock is brought from the surface of the moon,(A) its mass will change(B) its weight will change but not mass(C) both mass and weight will change(D) its mass and weight both will remain same.

*3.A body is weighed at the poles and then at the equator. The weight(A) at the equator will be greater than at the poles(B) at the poles will be greater than at the equator(C) at the poles will be equal to the weight at the equator(D) depends upon the shape of the object

4. A lead ball and a snow ball of identical radius are released from a certain height in vacuum. The time taken by both of them to reach the ground are(A) exactly equal(B) unequal(C) roughly equal(D) in the ratio of the density of lead and snow

5. The weight of a body at the centre of the earth is(A) zero (B) equal to its mass (C) maximum(D) infinite

*6. The SI unit of g is(A) m2/s (B) m/s2 (C) s/m2 (D) m/s

*7 The SI unit of G is(A) N2 m2/kg (B) N m2/kg (C) N m/kg (d) N m2/kg2

8. Choose the correct statement(A) All bodies repel each other in this universe.(B) Our earth does not behave like a magnet.(C) Acceleration due to gravity is 8.9 m/s2.(D) All bodies fall at the same rate in vacuum.

*9 The maximum weight of a body is(A) at the centre of the earth(B) inside the earth(C) on the surface of the earth(D) above the surface of the earth

10. If the distance between two masses be doubled, then the force between them will become(A) 1/4 times (B) 4 times (C) 1/2 times (D) 2 times

11. A body falls freely towards the earth with(A) uniform speed (B) uniform velocity (c) uniform acceleration(d) none of these

12. If the mass of a body is M on the surface of the earth, then its mass on the surface of the moon will be

(A) (B) M (C) M + 6 (D) M x 6

13. If a person jumps 1 m at the surface of the earth, he will jump 6 metres at the surface of the moon. Therefore, the ratio of moons acceleration due to gravity with respect to earths acceleration due to gravity would be(A) 6 (B) 1/6 (C) 0.6 (D) 0.06

14. Choose the correct statement:(A) Weight is a vector quantity.(B) The weight of a body in interplanetary space is maximum.(C) Weight increases when the bodies go up.(D) 1 N = 1 kg x 1 m/s15. The value of acceleration due to gravity near the earths surfe is(A) 8.9 m/s2 (B) 8.9 m/s (C) 9.8m/s2 (D) 9.8 m/s

* 16. The force of gravitation between two bodies does not depend upon(A) their separation (B) the gravitational constant (C) the product of their masses(D) the sum of their masses

17. The type of force which exists between charged bodies is(A) only gravitational (B) only electrical (C) neither gravitational nor electrical(D) both electrical and gravitational

18. When a fruit falls from a tree(A) only the earth attracts the fruit(B) both the earth and the fruit attract each other(C) only fruit attracts the earth(D) they repel each other

*19. When an object is thrown up, the force of gravity(A) acts in the direction of the motion(B) acts in the opposite direction of the motion(C) remains constant as the body moves up(D) increases as the body moves up

20. Newtons law of gravitation(A) can be verified in the laboratory (B) is valid only in the solar system (C) cannot be verified but is true(D) is valid only on earth

21. If the distance between two particles is halved, the gravitational force becomes(A) four times (B) two times(C) eight times (D) none of these

22. The force of gravitation exists(A) everywhere in the universe (B) at the surface of the earth only (C) inside the earth only (D) at the surface of the moon only

*23. Newtons law of gravitation holds good for(A) small bodies only(B) terrestrial bodies only (C) big bodies only(D) all types of bodies

24. The gravitational force is a(A) contact force (B) action-at-a-distance force (C) neither (a) nor (b)(D) both (a) and (b)

25. 1 kg wt is equal to(A) 9.8 N (B) 980 N (C) 98 N (D) 0.98 N

*26. 1 kg wt is equal to(A) 980 dyne (B) 9.80 dyne (C) 98 dyne (D) none of these

*27. Name the force responsible for the existence of the solar system:(A) force of friction (B) gravitational force (C) electrostatic force(D) magnetic force

28. Which of the following forces is responsible for the flow of water in rivers?(A) force of friction (B) gravitational force (C) electrostatic force(D) magnetic force

29. Name the force responsible for holding the atmosphere near the surface of theearth:(A) electrostatic force (B) magnetic force (C) frictional force(D) gravitational force

30. The value of G depends on(A) nature of the interacting bodies (B) size of the interacting bodies (C) mass of the interacting bodies (D) none of these

*31. The ratio of SI units to CGS units of G is(A) 103 (B) 102 (C) 10-2 (D) 10-3

*32. The ratio of SI units to CGS units of g is(A) 102 (B) 10 (C) 10 (D) 10-2

33. SI unit of C is Nm2 kg-2. Which of the following can also be used as the SI unit of G?(A) m3 kg-1 s-2 (B) m2 kg-2 s-1 (C) m kg-3 s-1 (D) m2 kg-3 s-2

34. The value of G depends on(A) the mass of the interacting bodies (B) the space where the particles are kept(C) the time at which the force is considered(D) none of these

*35 1 N is nearly equal to

(A) 0.1 kg wt (B) 1 kg wt (C) (D) 9.8 kg wt

36. The force of gravitation between two bodies can be zero if the separation between the bodies becomes(A) 1 (B) 0 (C) -1 (D) infinity

37. SI unit of acceleration due to gravity is(A) ms2 (B) ms-1 (C) N (D) N kg-1

38. Name the scientist who first performed Galileos experiment on the moon:(A) David Scott (B) Cavendish (C) Newton (D) none of these

39. Choose the correct statement.(A) Gravity and gravitation are same.(B) Gravity is a particular case of gravitation.(C) Acceleration due to gravity is a scalar quantity.(D) Different heavenly bodies have different values for G.

*40. The ratio of g00 to earth is

(A) 6 (B) (C) 4 (D)

41. In vacuum all freely falling bodies(A) have the same speed (B) have the same velocity (C) have the same force(D) have the same acceleration

42.At the centre of the earth, the value of g becomes(A) zero (B) unity (C) infinity (D) none of these

43. g is a vector and its direction is towards centre of the(A) body(B) sun(C) earth(D) any one of the above

44. The gravitational SI unit of weight is(A) kg wt (B) N (C) g wt (D) all the above

45. The gravitational force which acts on 1 kg is

(A) 9.8 N (B) (C) 980 N (D)

46. A body having a mass of 1 kg on the surface of the earth weighs

(A) 9.8 N (B) (C) 980 N (D)

47. A stone dropped from the roof of a building takes 4s to reach the ground. The height of the building is(A) 9.8 m (B) 19.6 m (C) 39.2 m (D) 78.4 m

48. A ball is thrown up and attains a maximum height of 100 m. Its initial speed was(A) 9.8 ms-1 (B) 44.2 ms-1 (C) 19.6 ms-1 (d) none of these

*49. Weight is(A) measured by a spring balance (b) measured by a beam balance (C) measured in kg(D) a scalar quantity

50. The weight of an object(A) is the quantity of the matter it contains(B) refers to its inertia(C) is same as its mass hut is expressed in different units (D) is the force with which it is attracted towards the earth

51. What is the mass of an object whose weight is 98 N?(A) 98 kg (B) 9.8 kg (C) 10 kg (d) none of these

*52. What is the mass of an object whose weight is 980 N?(A) 980 kg (B) 98 kg (C) 100 kg (D) zero

53. If the mass of a body is 5 kg, what is its weight?(A) 49 N (B) 5 N (C) 49 kg wt (D) none of these

54. How much would a 60 kg boy weigh on the moon?

Given: gmoon = (A) 10 kg wt (B) 6 kg wt (C) kg wt (D) zero

55. How much would a W kg man weigh on the moon in terms of gravitational units?(A) kg wt (B) 6W kg wt (C)W kg wt (D) zero

56. In Q 55 above, what would the man weigh in terms of absolute SI units?

(A) (Wg) N (B) (C) (6 Wg) N (D) zero

*57.A body has a mass M kg on the earth. What will be its weight on the earth?(A) Mg newton (B) newton (C) M newton (D) zero

58. What would be its weight on the moon in Q 57?

(A) (B) 6 M kg (C)(D) zero

59. What will be its mass on the moon in Q 57?

(A) M kg (B) 6 M kg (C) (D) zero

60. The gravitational pull exerted by the earth on a body is called its(A) true weight (B) mass (C) gravitational mass(D) inertial mass

61. A body weighs 60 kg on the earths surface. What would be its weight at the centre of the earth?(A) 60 kg wt (B) 6 kg wt (C) 60 x 9.8 kg wt (D) zero

*62. A weighing machine measures(A) weight only (B) mass only (C) mass and weight(D) none of these

63. A person stands on a weighing machine kept on the floor of an elevator When the elevator is at rest then the apparent weight of the person is(A) equal to his true weight (B) less than his true weight (C) more than his true weight(D) more or less than his true weight.

64. In Q 63 above, if the elevator moves down with a constant acceleration, the apparent weight of the person is(A) less than its true weight(B) equal to its true weight (C) more than its true weight(D) more or less than its true weight

65. In Q 63 above, if the elevator moves upward with a constant acceleration, the apparent weight of the person is(A) less than his true weight (B) equal to his true weight (C) more than his true weight(D) more or less than his true weight

66. In Q 64 above, suppose the cable breaks, then the weighing machine will read(A) more than the weight of the body (B) less than the weight of the body (C) equal to the weight of the body(D) zero

*67. Hold a stone at the end of a spring balance. The pointer shows 5 kg wt. Now release the spring balance. Then the pointer will read(A) more than 5 kg wt (B) less than 5 kg wt (C) equal to 5 kg wt(D) zero

68. The apparent weight of a body, weighing M kg wt, during free fall is(A) less than M kg wt (B) more than M kg wt (C) equal to M kg wt (D) zero

69. While orbiting around the earth in a spaceship, an astronaut experiences(A) more weight (B) lesser weight (C) weightlessness(D) nothing at all

*70. Which of the following motion is different from others?(A) A ball thrown horizontally in air.(B) A bomb released from a flying aeroplane.(C) A javelin thrown by an athlete.(D) A bird flying in the air.

71. An object thrown into space horizontally under the action of earths gravity is called a/an(A) projectile (B) trajectory (C) spaceship (D) none of these

*72. The path followed by a projectile is called its(A) trajectory (B) range (C) amplitude (D) none of these

*73. The horizontal distance travelled by a projectile is called its(A) trajectory (B) range (C) amplitude (D) none of these

74. If g is acceleration due to gravity, then the vertical distance travelled by a projectile in time t is equal to

(A) (B) (C) (D) none of these

75. The gravitational force between two objects placed at a distance r is proportional to

(A) r (B) r2 (C)(D) *76. The force of gravity on a body of mass W is

(A) W (B) Wg (C) (D) Wg277. When an object falls freely to the earth, the force of gravity is(A) opposite to the direction of motion(B) along the direction of motion(C) constant(D) zero78. Acceleration due to gravity of a body thrown up is(A) 9.8 ms-2 (B) - 9.8 ms-2 (C) 9.8 ms-2 (D) zero

*79.A bomb is released from a flying aeroplane. Its path will be(A) an arc of a circle (B) parabola (C) a zig-zag path(D) a straight vertical path in the down - word direction

80. The value of acceleration due to gravity dependes on(A) pressure (B) acceleration (C) force (D) none of these

81. The value of acceleration due to gavity depends on(A) mass of the body (B) radius of the body(C) shape of the body (D) mass of the earth

*82. If the symbols have their usual meanings, is equal to

(A) g2 (B) (C) g (D) 83. The time period of a geo-stationary satellite is(A) 24 hrs (B) 6 hrs (C) 365 days (D) none of these

84. The gravitational force between two stones of mass 1 kg each separated by a distance of 1 m in vacuum is(A) zero (B) 6.675 x 10-5 N (C) 6.675 x 10-8 N (D) 6.675 x 10-11 N

85. The weakest force of interaction is(A) electrostatic (B) gravitational (C) nuclear (D) electromagnetic

86. The time taken by a radiowave to go and come back after reflection from a communication satellite is

(A) (B) (C) 1 s (D)

*87. Weighlessness in a satellite is because of(A) intertia (B) zero gravity (C) centre of gravity(D) acceleration

88. The three laws of planetary motion were given by(A) Aristotle (B) Kepler (C) Copernicus (D) Tycho Brahe

89. From the quator to the poles, the value of g(A) decreases (B) increases (C) remains unchanged(D) first decreases then increases

*90. From the centre of the earth to the surface of the earth, the value of g varies with distance (r) as

(A) (B) (C) (D)

91. The value of g varies with distances (r) above the earths surface as

((A) (B) (C) (D) 92. The space in which a body experiences a force by virtue of its mass is called(A) magnetic field (B) electric field (C) gravitational field(D) none of these

93. The force experienced by a unit mass at a point in the gravitational field is called its(A) gravitational intensity (B) electric intensity (C) magnetic intensity(D) gravitational constant

94. The gravitational intensity in Q 93 is denoted by(A) g (B) G (C) E (D) none of these95. Which of the following represents the unit for gravitational intensity?(A) N (B) kg m-2 (C) N kg-1 (D) ms-3

96.Where will a body weigh minimum?(A) at a height of 100 m above the earths surface (B) at the earths surface(C) at a depth of 100 m below the earths surface (D) at the centre of the earth

*97.The variation of g with height or depth (r) is shown correctly by the graph in Fig. 3.4 (where R is radius of the earth),98. The value of gravitational intensity at the centre of the earth is(A) 1 (B) infinity (C) zero(D) can't be decided

99. The ratio of SI units to CGS of the gravitational intensity is(A) 103 (B) infinity (C) zero (D) 102

100. If the symbols have their usual meanings then represents

(A) G(B) G2(C) (D)

Answer

Q.12345678910

Ans.BBAAABDDCA

Q11121314151617181920

Ans.CBBACDDBBA

Q21222324252627282930

Ans.AADBAABBDD

Q31323334353637383940

Ans.AAADADA,DABB

Q41424344454647484950

Ans.DACAAADBAB

Q.51525354555657585960

Ans.CCAAABAAAA

Q61626364656667686970

Ans.DAAACDDDCD

Q71727374757677787980

Ans.AABACBBBBC

Q81828384858687888990

Ans.DCADBABBBB

Q.919293949596979899100

Ans.ACAACDACDA

WORK, ENERVGY AND POWER


1.Two unequal masses have the same K.E. Prove that the momentum of the heavier body is more.

2.Two unequal masses have the same momentum. Prove that the heavier body possesses lesser K.E.

3.A roller is pushed by applying a force of 50 N. The line of action of the force makes an angle of 60 with the horizontal. Find the work done in moving it through a distance of 10 m.Ans.250 J

4.Calculate the momentum of a body of mass 100 g having kinetic energy of 20 jouleAns.2kg m/s

5.Calculate the amount of work done in taking a packet of mass 100 kg to the top of a building of height 14.0 m. Take g = 10 m/s2.Ans.1.4 104 J

6. The momentum of a body increases by 20%. Calculate the percentage increase in its K.E.Ans.44%Sol.Initial momentum = mv

Final momentum = m

Initial K.E. =

Final K.E. =

% Increase in K.E = 7.The momentum of a body decreases by 20%. Calculate the percentage decrease in its K.E.Ans.36%

8.A bullet leaves a rifle with a velocity of 200 m/s and strikes a wooden target up to 4 cm. What velocity should it have to pierce the same block of wood up to 16 cm?Ans.400 m/s

9.The mass of a pendulum bob is 100g, and the string is 1 m long. The bob is held so that the string horizontal. It is then allowed to fall. Find the KE when the string makes an angle of (a) 0 (b) 30 with the vertical.Ans.(a) 98 105 erg; (b) 84 104 erg

10.What horsepower is necessary to lift 180 tonnes of coal per hour, from a mine 120 m deep?Ans.78.82 hp

11.An elevator lifts a load of 1250 kg through a height of 20 m in 5 s. Calculate the power of the elevator.Ans.49 kW

12.A bullet of mass 5 g leaves a rifle with a velocity of 2 m/s. If it strikes a wooden target and penetrates 20 cm into it, what is the average resistance offered by the target?Ans.5000 dynes

13.The human heart forces 4500 cc of blood per min through the arteries, under a pressure of 15 cm of Hg. Calculate the hp of the heart. Take 1 hp = 746 W and g = 980 cm/s2Ans.20 10-4 approx

14.A pump is required to lift 480 kg of water per mm. from a well 10 m deep, and eject it with a speed of 10 m/s.(A) How much work is done in lifting the water?(B) What is the magnitude of the K.E. given to water?(C) What is the horse power of the engine?Ans.(a) 47,040 J (b) 24,000 J (c) 1.6

15. A boy of mass 50 kg sits on a swing, suspended by a rope 5 m long. A person pulls the rope that makes an angle of 30 with the vertical. What is the gain in the gravitational potential energy of the boy? Ans. 328.3 J

16. A ball is dropped from rest from a height of 12 m. If the ball loses 25% of its K.E. on striking the ground, what is the height to which it bounces? How do you account for the loss in K.E. Ans. 9 m

17.17. A car of mass 1000 kg travels at 12 m/s on a horizontal and the resistance to motion is 500 N. Find (a) its momentum (b) its kinetic energy and (c) the power developed by the engine. Ans. (A) 1.2 x 104 Ns (b) 7.2 x 104 J (c) 6.0 kW

18. The brakes of an unloaded lorry of mass 1000 kg will slow it down from 40 to 20 km/h in 7.5 s. How long will they take to stop it from a speed of 30 km/h, if it has taken on a load of 2200 kg? Ans. 36 s

19. If the frictional force resisting the motion of a car is 300 N, find the work done (i.e, the energy expended) by a man who pushes the car at a steady rate for 25 m on a horizontal road. Ans. 7500 J

20. The propelling force of a rocket increases uniforily froni zero to 5 N in the first 12 m and remains constant for the next 40 m. Find the total work done.Ans. 2300

21. The potential energy stored in the wound-up spring of a toy motor-car is 18 J. Ignoring any frictional resistance to motion, find the distance this car (mass 200 g) will travel up a slope of 1 in 5. Ans. 45.9 cm

22. A body of mass 20 kg falls through a distance of 50 cm. What is the loss in P.E.?Ans.98 J

23. What is the power output of the sun if 4 x 10 kg of matter per second is converted into energy in the sun?Use E = mc2 , where c = 3 108 m/sHint:E = mc2 , where E represents energy per second

= 4 109 (3 108)2 = 3.6 1026 Js-1OrP = E = 3.6 1026 W

24.What is the ratio of 1 kWh to 1 Me V?Hint1 kWh = 3.6 106 J1 Me V = 106 1eV1 electron volt represents the energy associated with an electron when it jumps across a potential difference of 1 volt.1 eV = 1.602 10-19 C 1 volt

= 1.602 10-19 C = 1.602 10-19 Jor 1 MeV= 106 1.602 10-19 J= 1.602 10-13

= 2.25 101925(a) What is the amount of work done by a weight - lifter in holding a weight of 100 kg on his shoulders for 40 s ?(b) What is the amount of work done by a man pressing a rigid wall with a forece of 200 N?Ans.(a) zero (b) zero

26. In a tug of war, one team is slowly giving way to the other. What work is being done, and by whom?Hint:Work is done by the winning team. It is equal to the product of the resultant force applied by the two teams and the displacement that the losing team suffers.

27. A body is kept moving with uniform speed in a circle by a centripetal force acting on it. However, the work done by this force is zero. Is it true? Explain.

Hint: Work done = FS cos = FS cos 90 = 0

Because and are always at right angles to each other.

28. The earth moving round the sun in a circular orbit is acted upon by a force, and hence work must be done on the earth by this force. Do you agree with this statement?Hint:The statement is wrong. Work done is zero because the centripetal force cannot do any work on the earth.

29. A particle is moving in a circular path of given radius with[(i) constant (ii) increasing (iii) decreasing] number of rotations per second. What happens to work done in three cases?Hint:Work done = change in kinetic energy(i) For constant speed, kinetic energy does not change, and work done is zero.(ii) As K.E. is increasing, work is done by the external force.(iii) As K.E. is decreasing, work is done by the body on the force.

30. When a constant force is applied to a body moving with a constant acceleration, is power of the force constant? If not, how will force vary with speed for the power to be constant?Hint:Power = force x velocitySince the body has acceleration, therefore, velocity changes and power also changes. In order to keep the power constant, the force should vary inversely as velocity varies with time. In other words, if velocity increases with time then force should decrease with the same rate as the velocity is increasing.

31.Can a body have energy without having momentum?Hint:Yes, the body may have potential energy.

32. Can a body have momentum without having kinetic energy?Hint:No, it is not possible.

33. A meteorite burns in the atmosphere before it reaches the earths surface. What happens to its momentum?Hint:The momentum is transferred to the air molecules and the earth.

34. When a ball is thrown up, the magnitude of its momentum decreases and then increases. Does this violate the conservation of momentum principle?Hint:There is no violation of the conservation of momentum. The net momentum of the system (earth + ball + air molecules) always remains conserved.

35. If energy is neither created nor destroyed, what happens to the so much energy spent against friction?Hint:The energy lost against friction is dissipated in the form of heat and is not available for work.

36. A light and a heavy body have the same kinetic energy. Which one will have greater momentum?Hint:The heavy body.

37. A bullet is fired from a gun. Which will have greater kinetic energy: The bullet or the gun?Hint:The bullet has a greater kinetic energy.

38. A light and a heavy body have same momentum. Which one will have the greater kinetic energy?Hint:The lighter body.

39. State the work done in the following situations:(a) a person carrying bricks on his head on a level road from one place to another.(b) a man rowing a boat upstream at rest with respect to the shore.(c) when a body of mass rn moves with a uniform speed v in a circle.(d) when a car moves with a uniform speed on a smooth level road, neglecting the air resistance.Hint:(a) Work done in this case is zero because the angle between the force of gravity and displacement is 900.(b) The man is doing work because he is applying a force. It is because there is a relative motion between the boat and the stream.(c) Since force is always perpendicular to displacement, work done is zero.(d) Weight of the car and its displacement are at right angles, therefore, work done is zero.

40. A lorry and a car moving with same K.E. are brought to rest by the action of the brakes which provide equal retarding forces. Which of them will come to rest in a shorter distance?

F1S1 = F2S2

where F1, F2 are retarding forces produced by applying the brakes in the lorry and the car respectively and S1, S2 are their respective distances covered before they stop.From (i), F1S1 = F2S2As F1 = F2, we have S1 = S2.Therefore, before stopping they cover equal distances.

41. A ball is dropped vertically from rest at a height of 12 m. After striking the ground, it bounces to a height of 9 m. What fraction of kinetic energy does it lose on striking the ground?Hint:Let m be the mass of the body.When the body falls from some height, potential energy at the top equals the gain in kinetic energy. The body loses some kinetic energy and again rises to some different height.

Percentage loss in K.E. =

= 42. Two bodies of masses 1 kg and 4 kg have equal linear momentum. What is the ratio of their kinetic energies?

Hint: 43. A man whose mass is 75 kg walks up 10 steps, each 20 cm high, in 5 s. Find the power he develops. Take g = 10 ms-2.

Hint:Mass, m = 75 kg, Total height =

T = 5 S, Power =

44. A body of mass 10 kg is dropped from a height of 20 m. Find (i) its potential energy before it is dropped, (ii) its kinetic energy when it is 8 m above the ground and (iii) its kinetic energy when it hits the ground.Take g = 10ms-2Hint:(i) Potential energy = (10 10 20) J = 2000 J(ii) K.E. when it is 8 m above the ground = 1200 J(iii) K.E. when it hits the ground = 2000 J

45. A car of mass 2000 kg is lifted up a distance of 30 m by a crane in 1 minute. A second crane does the same job in 2 minutes. Do the cranes consume the same or different amounts of fuel? What is the power supplied by each crane? Neglect power dissipation against friction.Take g = 10 ms-Hint:Work done in lifting the car. W = mgh= 2000 10 30 = 6 105 JAccording to the principle of conservation of energy, both the cranes will consume the same amount of fuel equivalent to 6 105 J.

Power of first crane, P1 =

Power of 2nd crane, P2 = 46. A tube-well pumps out 2400 kg of water per minute. If water is coming out with a velocity of 3 ms-1, what is power of the pump? How much work is done, if the pump runs for 10 hours?

Hint:Mass of water pumped per second, Velocity of water, v = 3 ms-1

K.E. of water coming out per second =

Power of pump = 180 Js-1 = 180 WWork done = power time= 180 10 = 1800 Watt hour= 1800 3600 J = 6.48 106 J


I. MULTIPLE CHOICE QUESTIONSTick () the only correct choice amongst the following1. Work done upon a body is(A) a vector quantity (B) a scalar quantity (C) always positive(D) always negative

2. In the SI system, the unit of P.E. is(A) erg (B) dyne-cm (C) joule (D) none of these

3. Kilowatt hour (kWh) represents the unit of(A) power (B) impulse (C) momentum (D) none of these

4. Two unequal masses possess the same K.E. Then, the heavier mass has(A) greater momentum(B) smaller momentum(C) the same momentum as the lighter mass(D) greater speed

5. Two unequal masses possess the same momentum, then the kinetic energy of the heavier mass is ____________ the kinetic energy of the lighter mass.(A) same as (B) greater than (C) smaller than(D) much greater than

6. The speed of a motor car becomes six times, then the kinetic energy becomes(A) 6 times (B) 36 times (C) 12 times (D) 24 times

7. The number of joules contained in 1 kWh is(A) 36 x 102 (B) 36 x 103 (C) 36 x 104 (D) 3.6 x 106

8. A body is moved through a distance of 3 m in the following different ways. In which case is the maximum work done?(A) When pushed over an inclined plane.(B) When lifted vertically upward.(C) When pushed over smooth rollers.(D) When pushed on a plane, horizontal surface.

9. In the above example, the work done is minimum when the body is(A) pushed over an inclined plane(B) lifted vertically upward(C) pushed over the smooth rollers(D) pushed on a plane horizontal surface

10. A truck and a car are moving on a smooth, level road such that the K.E. associated with them is the same. Brakes are applied to both of them simultaneously. Which one will cover a greater distance before it stops?(A) Car (B) Truck (C) Both will cover the same distance(D) Nothing can be decided

11. A wound watch spring has energy.(A) mechanical (B) kinetic (C) potential(D) kinetic and potential

12. Two bullets P and Q, masses 10 and 20 g, are moving in the same direction towards a target with velocities of 20 and 10 m/s respectively. Which one of the bullets will pierce a greater distance through the target?(A) P (B) Q (C) both will cover the same distance (D) nothing can be decided

13. When the time taken to complete a given amount of work increases, then(A) power increases (B) power decreases (C) energy increases (D) energy decreases

14. When the force applied and the displacement of the body are inclined at 900 with each other, the work done is(A) infinite (B) maximum (C) zero (D) unity

15. A car is moving along a straight level road with constant speed. Then(A) the work done on the car is infinite(B) the work done on the car is zero(C) the work done on the car is a measure of the gravitational potential energy(D) the work done on the car cannot be found.

16. kgm-2s-2 represents the unit of(A) kinetic energy only (B) work done only (C) potential energy only(D) all the above

17. The moon revolves around the earth because the earth exerts a radial force on the moon. Does the earth perform work on the moon?(A) No(B) Yes, sometimes(C) Yes, always (D) cannot be decided

18. The K.E. of a body in increased most, by doubling its(A) mass (B) weight (C) speed (D) density

19. A body is dropped from a certain height from the ground. When it is halfway down, it possesses(A) only K.E. (B) both K.E. and RE. (C) only RE.(D) zero energy

20. A body of mass 20 kg is dropped from a height of 2 m. If g is taken to be equal to 10 m/s2, the kinetic energy of the body, just before striking the ground, will be(A) 400 J (B) 4 J (C) 40 J (D) none of these

21. The energy required to raise a given volume of water from a well can be in(A) megawatts (B) meganewton (C) megajoules (D) kilowatts

22. Two spherical balls of the same radius, but of different masses, are dropped at the same time from the top of a tower 19.6 m high. When they are 1.6 m above the ground, the balls will possess the same(A) K.E. (B) RE. (C) momentum (D) total energy

23. Asha lifts a doll from the floor and places it on a table. If the weight of the doll is known, what else does one need to know in order to calculate the work Asha has done on the doll?(A) The time required (B) Height of the table (C) Mass of the ball (D) Cost of the doll or the table

24. One kilowatt is approximately equal to(A) 1.30 hp (B) 1.56 hp(C) 2.50 hp(D) 1.83 hp

25. The work done in lifting a mass of 1 kg to a height of 9.8 m is(A) 1 J (B) (9.8)2 J (C) 9.8 J (D) none of these

26. Two bodies of equal weight are kept at heights of h and 1.5 h respectively. The ratio of their P.E. is(A) 3 : 2 (B) 2 : 3 (C) 1: 1(D) none of these

27. In which of the following cases will the work done be moved through a distance S on the ground. Fig. 4.7.(A) A (B) B (C) C (D) D

28. One of the rectangular components of a force of 50 N is gular component will be(A) 40 N (B) 30 N (C) 35 N(D) 45 N

29. The work done by a centripetal force(A) increases by decreasing the radius of the circle(B) decreases by increasing the radius of the circle(C) increases by increasing the mass of the body(D) is always zero

30. The units N-s are equivalent to(A) J (B) kg-m-s-1 (C) kg-m-s2(D) N -m - s

31. Certain weight is attached with a spring. It is pulled oscillates up and down. Its K.E. will be(A) maximum in the middle of the movement(B) maximum at the bottom(C) maximum just before it is released(D) constant

32. A photocell converts light energy into(A) chemical energy(B) electrical energy (C) electrical energy(D) mechanical energy

33.kWh represents the unit for(A) force (B) power(C) time(D) energy

34. Watt sec represents the unit for(A) energy (B) power(C) force(D) none of these

35.Energy cannot be measured in(A) Js (B) Ws(C) kWh(D) erg

36. A flying aeroplane has (A) only potential energy (B) only kinetic energy(C) both potential and kinetic energy(D) none of these

37. A steam engine converts(A) heat energy into sound energy (B) heat energy into mechanical energy (C) mechanical energy into heat energy (D) electrical energy into sound energy

38. A truck and a car are moving on a smooth level road such that the K.E. associated with them is the same. Which one will cover greater distance when brakes are applied to them simultaneously?(A) car (B) truck(C) both will cover the same distance(D) none of these

39. Mechanically work done is equal to (symbols have their usual meanings)(A) W = F/d (B) W = Fd (C) W = F + d (D) W = F- d

40. A body at rest can have(A) speed (B) energy (C) momentum (D) velocity

41. Which of the following graph best represents the graphical relation between momentum (p) and kinetic energy (k) for a body in motion? 42. When the momentum of a body increases by 10%, its K.E. increases by(A) 20% (B) 40% (C) 44%(D) none of these

43. When the momentum of a body decreases by 10%, its K.E. decreases by(A) 20 % (B) 40% (C) 36% (D) none of these

44. When the momentum of a body increases by 100%, its K.E. increases by(A) 20% (B) 40% (C) 100% (D) 300%

45. Which of the following physical quantity is different from others?(A) work (B) kinetic energy (C) force(D) potential energy

46. No work is said to have been done when an object moves at an angle of__________ with the direction of the force.(A) 0 (B) 90 (C) 180(D) between 90 and 180

47. A force of 20 N acts on a body and the body moves through 1 m at an angle of 45 to the direction of tne force. The work done by the force is

(A) (B)(C) (D) 48. When a body is whirled in a circle, the work done on it is(A) positive (B) negative (C) zero (D) infinite

49. The flowing water of a river possesses energy(A) gravitational (B) potential (C) electrical (D) kinetic

50. The unit of power is(A) watt per second (B) joule (C) kilojoule (D) watt

51. The mass of an object P is double the mass of Q. If both move with the same velocity, then the ratio of K.E. of P to that of Q is(A) 1: 2 (B) 2 : 1 (C) 1: 4 (D) 4 : 1

52. 1 hp is equal to(A) 0.746 kW (B) 7.46 kW (C) 74.6 kW (D) 746 kW

53. A bird flying in the sky has(A) K.E. only (B) P.E. only(C) neither K.E. nor P.E. (D) both K.E. and P.E.

54. A body rolling down a hill has(A) K.E. only (B) P.E. only (C) neither K.E. nor P.E.(D) both K.E. and P.E.

55. An object of mass 1 kg has a P.E. of 1 J relative to the ground when it is at a height of(A)

Numericals Class - IX TMH.docx

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