Mody Institute of Technology and Science, LakshmangarhFaculty of Engineering and TechnologyEnd Term Examination, Spring Semester - 2012-13 B. Tech. (ECE & EEE) Ist YearCourse Name: Engineering Mechanics Weight: 50 %Course Code: ME 105 Max. Marks: 100

Total No. of Printed Pages: 4 Time: 3 Hrs

Note: 1. Question number 1 is compulsory. Attempt five more questions out of the remaining seven (Questions 2 through 8) questions.

1. Choose correct answer[2*10]

i)The resultant of two forces of magnitude P each inclined at an angle of 600 with each other is a) 2P b) P c) d)

ii)The resultant of two forces can be defined as a force thata) keeps the system in equilibriumb) has the greatest magnitude in the systemc) has the same effect as the two forces d) has the same effect as one force

iii)The ratio between the tensions in the tight side and slack side of a flat belt drive increasesa) in direct proportion to the angle of lapb) exponentially as the angle of lap increasesc) in direct proportion to the coefficient of friction d) Proportional to the width of belt.

iv)The ratio of limiting friction and normal reaction is known asa) coefficient of friction b) angle of frictionc) angle of repose d) friction resistance

v)The centroid of a semi circular area of radius r is a) (r, 4r/3 ) b) ( r, 2r/) c) (r/, r) d) (r, r/2)

vi)Relation between E(Modulus of elasticity), K(Bulk modulus) and C (Modulus of rigidity) is given bya) E b) Ec) E d) E

vii)The rate of change of B.M is equal toa) shear force at that section b) deflection at that sectionc) loading at that section d) none of these

viii)A cantilever of span l has a load P acting at the free end. The bending moment at the support end will bea) zero b) PL c) d)

ix)The displacement of a point moving in a straight line is S =8t2+3t-5 (S is in m and t in s). The velocity when the displacement is zero, is a) 3m/s b) 13 m/s c) 16 m/s d) 12 m/s

x)A man in a lift will weigh more when the lift is a) Accelerated upwards b) Accelerated downwards c) Descends freely d) Lift going up is slowing down

2. a)State the law of triangle of forces and Lamis theorem. [6]

b)The plate is subjected to the two forces at A and B as shown. If 600, determine the magnitude of the resultant of these two forces and its direction measured from the horizontal.

Fig. 1[10]

3. a)With a neat diagram explain the following terms:Proportional limit, yield stress, upper yield point, elastic limit, ultimate stress of a material, elastic plastic zone. [8]

b)A member ABCD is subjected to point loads P1, P2, P3 and P4 as shown in figure. Calculate the force P3 necessary for equilibrium if P1 = 120kN, P2 = 220 kN and P4= 160 kN. Determine also the net change in length of the member. Take E = 2 x 105 N/mm2.

Fig. 2 [8]

4. a)Calculate the moment of inertia of the I-section as shown in Fig. 3 about the centroidal x0 and y0 axis. (All Dimensions are in mm.)1401080120

10

100

Fig. 3

[10]

b)Define the following terms:Moment of inertia, Radius of gyration, Centroid, Centre of mass, Centre of gravity, Polar moment of inertia. [6]

5. a)Define shear force and bending moment and also explain sagging and hogging in beam.

[6]

b)Draw Shear force diagram and Bending moment diagram for the simply supported beam as given in Fig 4.

Fig. 4 [10]

6. a)Draw a free body diagram of ladder resting on a rough surface and against rough wall. Identify unknowns in the problem and write the equations of equilibrium.

[6]

b)Determine the minimum horizontal force P required to hold the crate from sliding down the plane. The crate has a mass of 50 kg and the coefficient of static friction between the crate and the plane is = 0.25.

Fig. 5

[10]

7. a)What is a projectile motion? Derive an expression for the horizontal range, maximum height and time of flight.

[8]`

b)If a particles position is described by the polar coordinates r = 4(1 + sin t) m and = (2e-t) rad, where t is in seconds and the argument for the sine is in radians, determine the radial and transverse components of the particles velocity and acceleration when t = 2s.

[8]

8. a)State and explain DAlemberts principle. [4]

b)

c)State and derive the principle of work and energy relation.

Boxes A and B are at rest on a conveyor belt that is initially at rest. The belt is suddenly started in an upward direction so that slipping occurs between the belt and the boxes. Knowing that the coefficients of kinetic friction between the belt and the boxes are (k)A = 0.30 and (k)B = 0.32, determine the initial acceleration of each box.

Fig. 6

[4]

[8]

1 | Page