P-3 : COM, Rotational Dynamics & SHMapi.coachingapis.coachinglog.in/storage/162583/VS... · 2 (3) 2...
Transcript of P-3 : COM, Rotational Dynamics & SHMapi.coachingapis.coachinglog.in/storage/162583/VS... · 2 (3) 2...
1GCI
Class XIII (Spartan Batch)P-3 : COM, Rotational Dynamics & SHM
DTS (Diamond Test Series) for NEET-2020
1. The centre of mass of a body -
(1) Lies always at the geometrical centre
(2) Lies always inside the body
(3) Lies always outside the body
(4) May lie within or outside the body
2. Two particles of masses M and 2 M are at a distance D
apart. Under their mutual gravitational force they start
moving towards each other. The acceleration of their centre
of mass when they are D/2 apart is -
(1) 2GM/D2
(2) 4GM/D2
(3) 8GM/D2
(4) Zero
3. In fig a spherical part of radius R/2 is removed from a
bigger solid sphere of radius R. Assuming uniform mass
distribution, shift in the centre of mass from the centre of
main sphere will be -
(1) R
7
(2) R
14
(3)R
9
(4) R
3
4. Three masses are placed on the x–axis 300 g at origin,
500 g at x = 40 cm and 400 g at x = 70 cm. The distance of
the centre of mass from the origin is -
(1) 50 cm (2) 30 cm
(3) 40 cm (4) 45 cm
5. Moment of inertia plays the same role in rotatory motion
as in translatory motion is played by -
(1) velocity (2) acceleration
(3) mass (4) force
1.
(1)
(2)
(3)
(4)
2. M 2M D
D/2
(1) 2GM/D2
(2) 4GM/D2
(3) 8GM/D2
(4)
3. R R/2
(1) R
7
(2) R
14
(3)R
9
(4) R
3
4. x 300 g 500 g, x =
40 cm 400 g, x = 70 cm
(1) 50 cm (2) 30 cm
(3) 40 cm (4) 45 cm
5.
(1) (2)
(3) (4)
2GCI
Class XIII (Spartan Batch)P-3 : COM, Rotational Dynamics & SHM
DTS (Diamond Test Series) for NEET-2020
6. Three point masses, each m, are placed at the vertices of
an equilateral triangle of side 'a'. Moment of inertia of the
system about the axis COD which passes through the mass
at O and lies in the plane of triangle and perpendicular to
OA is -
(1) ma2
(2) 2
5ma2
(3) 9
4ma2
(4) 5
4ma2
7. The moment of inertia of a body does not depend on -
(1) the mass of the body
(2) the angular velocity of the body
(3) the axis of rotation of the body
(4) the distribution of the mass in the body
8. Which of the following has the smallest moment of inertia
about the central axis if all have equal mass and radii?
(1) Ring
(2) Disc
(3) Spherical shell
(4) Sphere
9. The moment of inertia of uniform circular disc of radius 'R'
and mass 'M' about an axis touching the disc at its
circumference and normal to the disc is -
(1) MR2
(2) 2
5MR2
(3) 3
2MR2
(4) 1
2MR2
6. 'a' m
COD COD,
O OA
(1) ma2
(2) 2
5ma2
(3) 9
4ma2
(4) 5
4ma2
7.
(1)
(2)
(3)
(4)
8.
(1)
(2)
(3)
(4)
9. 'R' 'M'
(1) MR2
(2) 2
5MR2
(3) 3
2MR2
(4) 1
2MR2
3GCI
Class XIII (Spartan Batch)P-3 : COM, Rotational Dynamics & SHM
DTS (Diamond Test Series) for NEET-2020
10. Figure, shows a uniform rectangular sheet with BC = 2AB.
Moment of inertia of the sheet is minimum about -
(1) AB
(2) PQ
(3) RS
(4) AD
11. A circular disc X of radius R is made from an iron plane of
thickness t and another disc Y of radius 4R is made from
an iron plate of thickness t/4. Then the relation between
the moment of inertia Ix and I
y about an axis passing through
its centre and perpendicular to its plane is -
(1) Iy = 32 I
x
(2) Iy = 16 I
x
(3) Iy = I
x
(4) Iy = 64 I
x
12. A thin circular ring of mass M and radius r is rotating about
an axis passing through its centre and perpendicular to its
plane with a constant angular velocity. Two objects, each
of mass m are attached gently to the opposite ends of a
diameter of the ring. The ring now rotates with angular
velocity -
(1) M m
M m
2
2
b g
(2) M(M – m)
(3) M m
M
2b g
(4) M
M m 2
13. A uniform heavy disc is rotating at constant angular velocity
() about a vertical axis through its centre O. Some wax W
is dropped gently on the disc. The angular velocity of the
disc -
(1) does not change (2) increase
(3) decreases (4) becomes zero
10. BC = 2AB
(1) AB
(2) PQ
(3) RS
(4) AD
11. X R t
Y 4R t/4
Ix
Iy
(1) Iy = 32 I
x
(2) Iy = 16 I
x
(3) Iy = I
x
(4) Iy = 64 I
x
12. m r
m
(1) M m
M m
2
2
b g
(2) M(M – m)
(3) M m
M
2b g
(4) M
M m 2
13. O
() W
(1) (2)
(3) (4)
4GCI
Class XIII (Spartan Batch)P-3 : COM, Rotational Dynamics & SHM
DTS (Diamond Test Series) for NEET-2020
14. A particle is moving along a straight line parallel to x–axis
with constant velocity. Angular momentum of particle about
the origin in vector form -
(1) mvbk (2) mvbk
(3) +mvak (4) -mvak
15. The moment of inertia of NaCI molecule with bond length r
about an axis perpendicular to the bond and passing through
the centre of mass is -
(1) m m rNa Clb g2
(2) m m
m mNa Cl
Na Cl
(3) m m
m mrNa Cl
Na Cl
2
(4) m m
m mrNa Cl
Na Cl
2
16. A smooth uniform rod of length L and mass M has identical
beads of negligible size, each of mass m, which can slide
freely along the rod. Initially the two beads are at the centre
of the rod and the system is rotating with angular velocity
0 about an axis perpendicular to the rod and passing
through the mid point of the rod., There are no external
forces. When the beads reach the ends of the rod, the
angular velocity of the rod would be -
(1) M
M m
0
2
(2) M
M m
0
4
(3) M
M m
0
6
(4) M
M m
0
8
14. x–
(1) mvbk (2) mvbk
(3) +mvak (4) -mvak
15. NaCI r
(1) m m rNa Clb g2
(2) m m
m mNa Cl
Na Cl
(3) m m
m mrNa Cl
Na Cl
2
(4) m m
m mrNa Cl
Na Cl
2
16. L M
m
0
(1) M
M m
0
2
(2) M
M m
0
4
(3) M
M m
0
6
(4) M
M m
0
8
5GCI
Class XIII (Spartan Batch)P-3 : COM, Rotational Dynamics & SHM
DTS (Diamond Test Series) for NEET-2020
17. On a smooth inclined plane a body of mass M is attached
between two springs. The other ends of the spring are
fixed with rigid supports. If each spring has a force constant
k, the period of oscillation of the body is -
(assuming the spring as massless)
k
kM
(1) 22
M
k
(2) 22
M
k
(3) 22
M
k
sin
(4) 22
M
k
sin
18. Acceleration-displacement graph of a particle executing
SHM Is as shown in given figure. The time period of its
oscillation is (in sec)
a(m/s )2
x(m)45º
(1) 2
(2) 2
(3)
(4) 4
17. M
k
( )
k
kM
(1) 22
M
k
(2) 22
M
k
(3) 22
M
k
sin
(4) 22
M
k
sin
18. SHM
( )
a(m/s )2
x(m)45º
(1) 2
(2) 2
(3)
(4) 4
6GCI
Class XIII (Spartan Batch)P-3 : COM, Rotational Dynamics & SHM
DTS (Diamond Test Series) for NEET-2020
19. Figure shows a flywheel of radius 10 cm. Its moment of
inertia about the rotation axis is 0.4 kg-m2. A massless
string passes over the flywheel and a mass 2 kg is attached
at its lower end. Angular acceleration of the pulley is nearly-
(1) 4.8 rad/s2
(2) 6.2 rad/s2
(3) 3.2 rad/s2
(4) 9.6 rad/s2
20. A unifrom disc of radius R is pivoted at point O on its
circumference. The time period of small oscillations about
an axis passing through O and perpendicular to plane of
disc will be -
(1) 2R
g
(2) 22
3
R
g
(3) 22
R
g
(4) 23
2
R
g
21. A particle executes SHM. Its velocities are v1 and v2 at
displacements x1 and x2 from mean position respectively.
The frequency of oscillation will be -
(1) 1
212
22
12
22
1 2
v v
x x
L
NMM
O
QPP
/
(2) 1
212
22
22
12
1 2
v v
x x
L
NMM
O
QPP
/
(3) 1
212
22
12
22
1 2
x x
v v
L
NMM
O
QPP
/
(4) 1
222
12
12
22
1 2
x x
v v
L
NMM
O
QPP
/
19. 10 cm
0.4 kg-m2
2 kg
(1) 4.8 rad/s2
(2) 6.2 rad/s2
(3) 3.2 rad/s2
(4) 9.6 rad/s2
20. R
O O
(1) 2R
g
(2) 22
3
R
g
(3) 22
R
g
(4) 23
2
R
g
21. x1 x2
v1 v2
(1) 1
212
22
12
22
1 2
v v
x x
L
NMM
O
QPP
/
(2) 1
212
22
22
12
1 2
v v
x x
L
NMM
O
QPP
/
(3) 1
212
22
12
22
1 2
x x
v v
L
NMM
O
QPP
/
(4) 1
222
12
12
22
1 2
x x
v v
L
NMM
O
QPP
/
7GCI
Class XIII (Spartan Batch)P-3 : COM, Rotational Dynamics & SHM
DTS (Diamond Test Series) for NEET-2020
22. An object suspended from a spring exhibits oscillations of
period T. Now the spring is cut in two halves and the same
object is suspsended with two halves as shown in figure.
The new time period of oscillation will become -
(1) T
2
(2) 2T
(3) T
2
(4) T
2 2
23. A particle of mass m is located in a potential field given by
U(x) = U0 (1– cos ax) where U0 and a are constants. The
period of small oscillations is -
(1) 2 U
ma
02
(2) 2 mU
a
02
(3) 2 a
mU
2
0
(4) 2 m
U a02
24. The time period of a simple pendulum having infinite length
is -
(1)
(2) 2 R g/
(3) 2 2 R g/
(4) 2 2 / g
22. T
(1) T
2
(2) 2T
(3) T
2
(4) T
2 2
23. m U(x) = U0 (1- cos ax)
U0 a -
(1) 2 U
ma
02
(2) 2 mU
a
02
(3) 2 a
mU
2
0
(4) 2 m
U a02
24.
(1)
(2) 2 R g/
(3) 2 2 R g/
(4) 2 2 / g
8GCI
Class XIII (Spartan Batch)P-3 : COM, Rotational Dynamics & SHM
DTS (Diamond Test Series) for NEET-2020
25. A ring or radius 3a is fixed rigidly on a table. A small ring
whose mass is m and radius a, rolls without slipping inside
it as shown in the figure. The small ring is released from
position A. When it reaches at the lowest point, the speed
of the centre of the ring at that time would be -
(1) 2ga
(2) 3ga
(3) 6ga
(4) 4ga
26. Two discs have same mass and thickness. Their materials
are of densities 1 and 2 . The ratio of their moment of
inertia about central axis will be -
(1) 1 : 2
(2) 1 2 : 1
(3) 1 : 1 2
(4) 2 : 1
27. A wheel is rolling uniformly along a level road (see figure).
The speed of transitional motion of the wheel axis is V.
What are the speeds of the points A and B on the wheel
rim relative to the road at the instant shown in the figure -
(1) VA = V ; VB = 0
(2) VA = 0; VB = V
(3) VA = 0 ; VB = 0
(4) VA = 0; VB = 2V
25. 3a
m a
(1) 2ga
(2) 3ga
(3) 6ga
(4) 4ga
26.
1 2
(1) 1 : 2
(2) 1 2 : 1
(3) 1 : 1 2
(4) 2 : 1
27.
V
A B
(1) VA = V ; VB = 0
(2) VA = 0; VB = V
(3) VA = 0 ; VB = 0
(4) VA = 0; VB = 2V
9GCI
Class XIII (Spartan Batch)P-3 : COM, Rotational Dynamics & SHM
DTS (Diamond Test Series) for NEET-2020
28. A body of radius R and mass m is rolling on a horizontal
plane without slipping with speed v. It then rolls up a hill of
vertical height h. If h = 3v2/4g, the body is -
(1) Ring
(2) Cylinder
(3) Solid sphere
(4) Spherical shell
29. Angular Momentum is -
(1) a polar vector
(2) an axial vector
(3) a scalar
(4) none of these
30. A uniform solid cylinder of mass M and radius R rotates on
a horizontal, frictionless axel. Two masses hung from light
cords wrapped around the cylinder. If the system is released
from rest, the tension in each cord is -
(1) Mmg
M m( ) (2) Mmg
M m( ) 2
(3) Mmg
m m( ) 3(4)
Mmg
M m( ) 4
31. Three particles are connected by light, rigid rods lying along
the y-axis. If the system rotates about the x-axis with an
angular speed of 2rad/s, the M.I. of the system is -
(1) 46 kg-m2 (2) 92kg-m2
(3) 184 kg-m2 (4) 276 kg-m2
28. m R v
h
h = 3v2/4g
(1)
(2)
(3)
(4)
29.
(1)
(2)
(3)
(4)
30. M R
(1) Mmg
M m( ) (2) Mmg
M m( ) 2
(3) Mmg
m m( ) 3(4)
Mmg
M m( ) 4
31. y-
x- 2
(1) 46 kg-m2 (2) 92kg-m2
(3) 184 kg-m2 (4) 276 kg-m2
10GCI
Class XIII (Spartan Batch)P-3 : COM, Rotational Dynamics & SHM
DTS (Diamond Test Series) for NEET-2020
32. A particle is oscillating in SHM. What fraction of total energy
is kinetic when the particle is at A/2 (A = Amplitude) from
the mean position
(1) 3
4
(2) 2
4
(3) 4
7
(4) 5
7
33. The time period of a simple pendulum of length L as
measured in an elevator descending with accelerationg
3
is -
(1) 23L
g
(2) 3L
g
F
HG
I
KJ
(3) 23
2
L
g
F
HG
I
KJ
(4) 22
3
L
g
34. The angular frequency of motion whose equation is
42
2
d y
dt + 9y = 0 is (y = displacement and t = time)
(1) 9
4(2)
4
9
(3) 3
2(4)
2
3
35. A simple pendulum is taken from the equator to the pole.
Its period -
(1) Decrease
(2) Increase
(3) Remains the same
(4) Decrease and then increases
32.
A/2 (A = )
(1) 3
4
(2) 2
4
(3) 4
7
(4) 5
7
33.g
3 L
(1) 23L
g
(2) 3L
g
F
HG
I
KJ
(3) 23
2
L
g
F
HG
I
KJ
(4) 22
3
L
g
34. 42
2
d y
dt + 9y = 0
(y = t = )
(1) 9
4(2)
4
9
(3) 3
2(4)
2
3
35.
(1)
(2)
(3)
(4)
11GCI
Class XIII (Spartan Batch)P-3 : COM, Rotational Dynamics & SHM
DTS (Diamond Test Series) for NEET-2020
36. The dimensions of moment of intertia is -
(1) [M1L2T–1]
(2) [M0L–2T0]
(3) [M0L2T2]
(4) [M1L2T0]
37. If a spring has time period T, and is cut into n equal parts,
then the time period of each part will be -
(1) T n
(2) T
n
(3) nT
(4) T
38. Four massless springs whose force constants are 2k, 2k, k
and 2k respectively are attached to a mass M kept on a
frictionless plane (as shown in figure). If the mass M is
displaced in the horizontal direction, then the frequency of
the system -
2k 2k
2k
k
M
(1) 1
2 4k
M
(2) 1
2
4
k
M
(3) 1
2 7k
M
(4) 1
2
7
k
M
39. The amplitude of a particle executing simple harmonic
motion is a. At what displacement the kinetic energy will
be equal to the potential energy -
(1) zero (2) a/2
(3) a/ 2 (4) 3a/4
36.
(1) [M1L2T–1]
(2) [M0L–2T0]
(3) [M0L2T2]
(4) [M1L2T0]
37. T n
(1) T n
(2) T
n
(3) nT
(4) T
38. 2k, 2k, k 2k
M M
2k 2k
2k
k
M
(1) 1
2 4k
M
(2) 1
2
4
k
M
(3) 1
2 7k
M
(4) 1
2
7
k
M
39. a
(1) (2) a/2
(3) a/ 2 (4) 3a/4
12GCI
Class XIII (Spartan Batch)P-3 : COM, Rotational Dynamics & SHM
DTS (Diamond Test Series) for NEET-2020
40. A thin wire of length L and uniform linear mass density is
bent into a circular loop with centre at O as shown in figure.
The moment of inertia of the loop about the axis XX' is-
(1)
L3
28(2)
L3
216(3)
5
16
3
2
L (4)
3
8
3
2
L
41. A particle is moving in a circle with uniform speed. Its motion is
(1) aperiodic
(2) periodic and simple harmonic
(3) periodic but not simple harmonic
(4) none of the above
42. Given
F i j 4 10 e j and
r i j 5 3
e j , compute torque.
(1) 62j unit (2) 62 k unit
(3) 48 i unit (4) 48 k unit
43. The initial angular velocity of fly wheel of moment of inertia
2Kg-m2, is 50 radian/sec. A torque of 10 N-m acts on it.
The time in which it gets accelerated to 80 radians/sec will
be -
(1) 12 sec (2) 2 sec
(3) 6 sec (4) 8 sec
44. If Kr and K
t refers to rotational and translational K.E. of an
object in pure rolling motion respectively then true
statement are -
(1) For disc Kr = 50% of K
t
(2) For shell Kr = 33% of K
t
(3) For solid sphere Kr = 50% of K
t
(4) None of these
45. Out of the two eggs, both equal in weight and indentical in
shape and size, one is raw and the other is half boiled. The
ratio between the moment of inertia of raw to boiled one,
about a central axis, will be -
(1) one (2) greather than one
(3) less than one (4) none of these
40. L
O
XX'
(1)
L3
28(2)
L3
216(3)
5
16
3
2
L(4)
3
8
3
2
L
41.
(1)
(2)
(3)
(4)
42. r i j 5 3
e j r i j 5 3
e j ,
(1) 62j (2) 62 k
(3) 48 i (4) 48 k
43. 2Kg-m2 50
radian/sec 10 N-m
80 radians/sec
(1) 12 sec (2) 2 sec
(3) 6 sec (4) 8 sec
44. Kr
Kt
(1) Kr = K
t 50%
(2) Kr = K
t 33%
(3) Kr = K
t 50%
(4)
45.
(1) (2)
(3) (4)