Prayas JEE (2025)
MANTHAN & ABDEHYA
Physics Rotational Motion
Exercise-1 6. A body is in pure rotation. The linear speed v of a particle,
the distance r of the particle from the axis and the angular
ANGULAR DISPLACEMENT, VELOCITY AND v
velocity ω of the body are related as ω = . Thus:
r
ACCELERATION 1
(a) ω ∝
1. Two bodies of mass 10 kg and 5 kg moving in concentric r
orbits of radius r1 and r2such that their periods are same. (b) ω ∝ r
The ratio of centripetal accelerations is (c) ω = 0
æ ö
r æ ö
r (d) ω is independent of r.
(a) çç 1 ÷÷÷ (b) çç 2 ÷÷÷
çè r ÷ø çè r ÷ø
2 1
æ r1 ÷ö3 æ r2 ÷ö2 MOMENT OF INERTIA
(c) çç ÷÷ ç
(d) ç ÷÷
çè r ÷ø çè r ÷ø 7. Four masses are fixed on a massless rod as shown in fig.
2 1
The moment of inertia about the axis P is nearly
2. A wheel starts rotating from rest and attains an angular
P
velocity of 60 rad/sec in 5 seconds. The total angular
displacement in radians will be- 2 kg 5 kg 5 kg 2 kg
(a) 60 (b) 80 (c) 100 (d) 150 0.2m 0.2m 0.2m 0.2m
3. Figure shows a small wheel fixed coaxially on a bigger one
of double the radius. The system rotates uniformly about the (a) 2 kg m2 (b) 1 kg m2
common axis. The strings supporting A and B do not slip on
(c) 0.5 kg m2 (d) 0.3 kg m2
the wheels. If x and y be the distances travelled by A and B
in the same time interval, then- 8. By the theorem of perpendicular axes, if a body be in X–Z-
plane then:
(a) Ix – Iy = Iz (b) Ix + Iz = Iy
(c) Ix + Iy = Iz (d) Iy + Iz = Ix
9. The axis X and Z in the plane of a disc are mutually
A perpendicular and Y-axis is perpendicular to the plane of
B
the disc. If the moment of inertia of the body about X and Y
(a) x = 2y (b) x = y axes is respectively 30 kg m2 and 40 kg m2 then M .I. about
(c) y = 2x (d) None of these Z-axis in kg m2 will be:
(a) 70 (b) 50
4. The linear and angular acceleration of a particle are
(c) 10 (d) Zero
10 m /sec2 and 5 rad/sec2 respectively It will be at a distance
from the axis of rotation. 10. Two rods each of mass m and length are joined at the centre
1 to form a cross. The moment of inertia of this cross about
(a) 50 m (b) m (c) 1 m (d) 2 m an axis passing through the common centre of the rods and
2
5. A particle is moving with a constant angular velocity about perpendicular to the plane formed by them, is:
an exterior axis. Its linear velocity will depend upon - m 2 m 2
(a) (b)
(a) perpendicular distance of the particle form the axis 12 6
(b) the mass of particle
m 2 m 2
(c) angular acceleration of the particle (c) (d)
3 2
(d) the linear acceleration of particle
1
,11. For the same total mass which of the following will have the 7 14
largest moment of inertia about an axis passing through the (a) MR2 (b) MR2
2 5
centre of mass and perpendicular to the plane of the body
16 21
(a) A disc of radius a (c) MR2 (d) MR2
5 5
(b) A ring of radius a 19. The moment of inertia of a square lamina about the
(c) A square lamina of side 2a perpendicular axis through its centre of mass is 20 kg-m2.
Then the moment of inertia about an axis touching its side
(d) Four rods forming a square of side 2a and in the plane of the lamina will be:
12. The moment of inertia of a thin uniform circular disc about (a) 10 kg-m2 (b) 30 kg-m2
one of the diameters is I. Its moment of inertia about an axis (c) 40 kg-m 2 (d) 25 kg-m2
perpendicular to the plane of disc and passing through its 20. Three rings, each of mass P and radius Q are arranged
centre is: as shown in the figure. The moment of inertia of the
(a) ( 2)I (b) 2I (c) I/2 (d) I / 2
arrangement about YY’ axis will be:
Y
13. The moment of inertia of a uniform semicircular wire of 1 2
mass M and radius r about a line perpendicular to the plane Q Q
of the wire through the centre is: P P
1 2
(a) Mr2 (b) Mr Q
2
1 2 2 2
(c) Mr (d) Mr 3 P
4 5 Y'
14. The density of a rod AB increases linearly from A to B. Its
midpoint is O and its centre of mass is at C. Four axes pass 7 2
(a) PQ2 (b) PQ2
through A, B, O and C, all perpendicular to the length of the 2 7
rod. The moments of inertia of the rod about these axes are
2 5
IA, IB, IO and IC respectively. (c) PQ2 (d) PQ2
5 2
(a) IA > IB (b) IA< IB
(c) IO= IC (d) IO < IC 21. The moment of inertia of a rod of mass M and length L about
15. A stone of mass 4 kg is whirled in a horizontal circle of radius an axis passing through one edge and perpendicular to its
1m and makes 2 rev/sec. The moment of inertia of the stone length will be:
about the axis of rotation is-
ML2 ML2
(a) 64 kg × m2 (b) 4 kg × m2 (a) (b)
12 6
(c) 16 kg × m2 (d) 1 kg × m2
16. In an arrangement four particles, each of mass 2 units are ML2
(c) (d) ML2
situated at the coordinate points (3, 2, 0), (1, –1, 0), (0, 0, 0) 3
and (–1, 1, 0). The moment of inertia of this arrangement 22. Three thin uniform rods each of mass M and length L and
about the Z-axis will be-
placed along the three axis of a Cartesian coordinate system
(a) 8 units (b) 16 units
(c) 43 units (d) 34 units with one end of each rod at the origin. The M.I. of the system
about z-axis is:
17. A solid sphere and a hollow sphere of the same mass have
the same M.I. about their respective diameters. The ratio of ML2 2 ML2
their radii will be : (a) (b)
3 3
(a) 1 : 2 (b) 3: 5 ML2
(c) (d) ML2
(c) 5: 3 (d) 5 : 4 6
18. Three solid spheres of mass M and radius R are shown in 23. Four particles each of mass m are placed at the corners
the figure. The moment of inertia of the system about XX’ of a square of side length .The radius of gyration of the
axis wil be: system about an axis perpendicular to the square and passing
X
through centre is:
(a) (b)
2 2
(c) (d) 2
X'
2
, 24. The M.I. of a thin rod of length about the perpendicular
axis through its centre is I. The M.I. of the square structure
( ) (
29. Aforce of 2iˆ − 4 ˆj + 2kˆ Newton acts at a point 3iˆ + 2 ˆj − 4kˆ )
made by four such rods about a perpendicular axis to the metre from the origin. The magnitude of torque is:
plane and through the centre will be: (a) zero (b) 24.4 N-m
(a) 4 I (b) 8 I (c) 0.244 N-m (d) 2.444 N-m
30. Rate of change of angular momentum with respect to time
(c) 12 I (d) 16 I
is proportional to :
25. The moment of inertia of a ring of mass M and radius R (a) angular velocity (b) angular acceleration
about PQ axis will be: (c) moment of inertia (d) torque
D 31. When constant torque is acting on a body then:
P
(a) body maintain its state or moves in straight line with
M same velocity
(b) acquire linear acceleration
R (c) acquire angular acceleration
O O' (d) rotates with a constant angular velocity
32. If I = 50 kg-m2, then how much torque will be applied to
stop it in 10 sec. Its initial angular speed is 20 rad/sec:
(a) 100 N-m (b) 150 N-m
D' Q (c) 200 N-m (d) 250 N-m
MR 2 33. A particle is at a distance r from the axis of rotation. A given
(a) MR2 (b) torque τ produces some angular acceleration in it. If the mass
2
of the particle is doubled and its distance from the axis is
(c) 3/2MR2 (d) 2MR2 halved, the value of torque to produce the same angular
26. Four point masses (each of mass m) are arranged in the acceleration is:
X – Y plane the moment of inertia of this array of masses (a) τ/2 (b) τ (c) 2τ (d) 4τ
about Y-axis is ENERGY ANALYSIS
Y 34. A ring of radius r and mass m rotates about an axis passing
a (a,a)
through its centre and perpendicular to its plane with angular
a (2a,0) velocity ω. Its kinetic energy is
O a X
(0,0) 1 1 2 2
a (a) mrω (b) mrω2 (c) mr2ω2 (d) mr ω
(a,–a) 2 2
35. A rod of length L is hinged at one end. It is brought to a
(a) ma2 (b) 2ma2 horizontal position and released. The angular velocity of
(c) 4ma2 (d) 6ma2 the rod when it is in vertical position is
(a) 2 g / L (b) 3 g / L (c) g / 2 L (d) g/L
FIXED AXIS ROTATION , TOPPLING
36. Two bodies A and B having same angular momentum and
27. For a system to be in equilibrium, the torques acting on it
IA > IB, then the relation between (K.E.)A and (K.E.)B will be:
must balance. This is true only if the torques are taken about
(a) the centre of the system (a) (K.E.)A > (K.E.)B (b) (K.E.)A = (K.E.)B
(b) the centre of mass of the system (c) (K.E.)A < (K.E.)B (d) (K.E.)A ≤ (K.E.)B
(c) any point on the system
(d) any point on the system or outside it ANGULAR MOMENTUM
28. A rectangular block has a square base measuring a × a, and 37. A thin circular ring of mass M and radius r is rotating about
its height is h. It moves on a horizontal surface in a direction its axis with a constant angular velocity ω. Two objects,
perpendicular to one of the edges h being vertical. The each of mass m are attached gently to the opposite ends of a
coefficient of friction is µ. It will topple if
diameter of the ring. The wheel now rotates with an angular
h a velocity
(a) µ > (b) µ >
a h ωM ω ( M − 2m )
2a a (a) ( M + m) (b) ( M + 2m )
(c) µ > (d) µ >
h 2h ωM ω ( M + 2m )
(c) ( M + 2m ) (d)
M
3
, 38. A rotating table completes one rotation in 10 sec and its 46. One hollow and one solid cylinder of the same outer radius
moment of inertia is 100 kg-m2. A person of 50 kg mass rolls down on a rough inclined plane. The foot of the inclined
stands at the centre of the rotating table. If the person moves plane is reached by
2m. from the centre, the angular velocity of the rotating table (a) solid cylinder earlier
in rad/sec. will be: (b) hollow cylinder earlier
2π 20π (c) simultaneously
(a) (b)
30 30 (d) the heavier earlier irrespective of being solid or hollow
2π 47. If a solid sphere, disc and cylinder are allowed to roll down
(c) (d) 2 π
3 an inclined plane from the same height
39. A uniform heavy disc is rotating at constant angular velocity (a) cylinder will reach the bottom first
(ω) about a vertical axis through its centre O. Some wax is (b) disc will reach the bottom first
dropped gently on the disc. The angular velocity of the disc: (c) sphere will reach the bottom first
(a) does not change (b) increases (d) all will reach the bottom at the same time
(c) decreases (d) becomes zero 48. A solid homogeneous sphere is moving on a rough horizontal
40. A girl sits near the edge of a rotating circular platform. If surface, partly rolling and partly sliding. During this kind of
the girl moves from circumference towards the centre of the motion of the sphere
platform then the angular velocity of the platform will: (a) total kinetic energy is conserved
(a) decrease (b) increase (b) angular momentum of the sphere about the point of
(c) remain same (d) becomes zero contact with the plane is conserved
41. Two wheels P and Q are mounted on the same axle. The (c) only the rotational kinetic energy about the centre of
moment of inertia of P is 6 kg-m2 and it is rotating at 600 mass is conserved
rotations per minute and Q is at rest. If the two are joined (d) angular momentum about centre of mass is conversed
by means of a clutch then they combined and rotate at 400
rotations per minute. The moment of inertia of Q will be - 49. A ring of mass M is kept on a horizontal rough surface.
(a) 3 kg-m2 (b) 4 kg-m2 A force F is applied tangentially at its rim as shown. The
(c) 5 kg-m 2 (d) 8 kg-m2 coefficient of friction between the ring and the surface is µ.
Then
COMBINED ROTATION AND TRANSLATION F
42. If a spherical ball rolls on a table without slipping, the fraction
of its total kinetic energy associated with rotation is
(a) 3/5 (b) 2/7
f
(c) 2/5 (d) 3/7
(a) friction will act in the forward direction
43. The speed of a homogeneous solid sphere after rolling down
an inclined plane of vertical height h, from rest without (b) friction will act in the backward direction
sliding is (c) frictional force will not act
(a) gh (b) ( g / 5) gh (d) frictional force will be µ Mg.
50. A ring takes time t1 and t2 for sliding down and rolling down
(c) ( ) gh (d) ()gh
an inclined plane of length L respectively for reaching the
44. The rotational kinetic energy of a body is E. In the absence
bottom. The ratio of t1 and t2 is:
of external torque, if mass of the body is halved and radius
of gyration doubled, then its rotational kinetic energy will be: (a) 2:1 (b) 1 : 2 (c) 1 : 2 (d) 2 : 1
(a) 0.5 E (b) 0.25E 51. A ladder rests against a frictionless vertical wall, with its
(c) E (d) 2E upper end 6 m above the ground and the lower end 4 m away
45. A ring is rolling without slipping. Its energy of translation from the wall. The weight of the ladder is 500 N and its C.G.
is E. Its total kinetic energy will be: at 1/3rd distance from the lower end. Wall’s reaction will be,
(a) E (b) 2E (in Newton)
(c) 3E (d) 4E (a) 111 (b) 333 (c) 222 (d) 129
4
MANTHAN & ABDEHYA
Physics Rotational Motion
Exercise-1 6. A body is in pure rotation. The linear speed v of a particle,
the distance r of the particle from the axis and the angular
ANGULAR DISPLACEMENT, VELOCITY AND v
velocity ω of the body are related as ω = . Thus:
r
ACCELERATION 1
(a) ω ∝
1. Two bodies of mass 10 kg and 5 kg moving in concentric r
orbits of radius r1 and r2such that their periods are same. (b) ω ∝ r
The ratio of centripetal accelerations is (c) ω = 0
æ ö
r æ ö
r (d) ω is independent of r.
(a) çç 1 ÷÷÷ (b) çç 2 ÷÷÷
çè r ÷ø çè r ÷ø
2 1
æ r1 ÷ö3 æ r2 ÷ö2 MOMENT OF INERTIA
(c) çç ÷÷ ç
(d) ç ÷÷
çè r ÷ø çè r ÷ø 7. Four masses are fixed on a massless rod as shown in fig.
2 1
The moment of inertia about the axis P is nearly
2. A wheel starts rotating from rest and attains an angular
P
velocity of 60 rad/sec in 5 seconds. The total angular
displacement in radians will be- 2 kg 5 kg 5 kg 2 kg
(a) 60 (b) 80 (c) 100 (d) 150 0.2m 0.2m 0.2m 0.2m
3. Figure shows a small wheel fixed coaxially on a bigger one
of double the radius. The system rotates uniformly about the (a) 2 kg m2 (b) 1 kg m2
common axis. The strings supporting A and B do not slip on
(c) 0.5 kg m2 (d) 0.3 kg m2
the wheels. If x and y be the distances travelled by A and B
in the same time interval, then- 8. By the theorem of perpendicular axes, if a body be in X–Z-
plane then:
(a) Ix – Iy = Iz (b) Ix + Iz = Iy
(c) Ix + Iy = Iz (d) Iy + Iz = Ix
9. The axis X and Z in the plane of a disc are mutually
A perpendicular and Y-axis is perpendicular to the plane of
B
the disc. If the moment of inertia of the body about X and Y
(a) x = 2y (b) x = y axes is respectively 30 kg m2 and 40 kg m2 then M .I. about
(c) y = 2x (d) None of these Z-axis in kg m2 will be:
(a) 70 (b) 50
4. The linear and angular acceleration of a particle are
(c) 10 (d) Zero
10 m /sec2 and 5 rad/sec2 respectively It will be at a distance
from the axis of rotation. 10. Two rods each of mass m and length are joined at the centre
1 to form a cross. The moment of inertia of this cross about
(a) 50 m (b) m (c) 1 m (d) 2 m an axis passing through the common centre of the rods and
2
5. A particle is moving with a constant angular velocity about perpendicular to the plane formed by them, is:
an exterior axis. Its linear velocity will depend upon - m 2 m 2
(a) (b)
(a) perpendicular distance of the particle form the axis 12 6
(b) the mass of particle
m 2 m 2
(c) angular acceleration of the particle (c) (d)
3 2
(d) the linear acceleration of particle
1
,11. For the same total mass which of the following will have the 7 14
largest moment of inertia about an axis passing through the (a) MR2 (b) MR2
2 5
centre of mass and perpendicular to the plane of the body
16 21
(a) A disc of radius a (c) MR2 (d) MR2
5 5
(b) A ring of radius a 19. The moment of inertia of a square lamina about the
(c) A square lamina of side 2a perpendicular axis through its centre of mass is 20 kg-m2.
Then the moment of inertia about an axis touching its side
(d) Four rods forming a square of side 2a and in the plane of the lamina will be:
12. The moment of inertia of a thin uniform circular disc about (a) 10 kg-m2 (b) 30 kg-m2
one of the diameters is I. Its moment of inertia about an axis (c) 40 kg-m 2 (d) 25 kg-m2
perpendicular to the plane of disc and passing through its 20. Three rings, each of mass P and radius Q are arranged
centre is: as shown in the figure. The moment of inertia of the
(a) ( 2)I (b) 2I (c) I/2 (d) I / 2
arrangement about YY’ axis will be:
Y
13. The moment of inertia of a uniform semicircular wire of 1 2
mass M and radius r about a line perpendicular to the plane Q Q
of the wire through the centre is: P P
1 2
(a) Mr2 (b) Mr Q
2
1 2 2 2
(c) Mr (d) Mr 3 P
4 5 Y'
14. The density of a rod AB increases linearly from A to B. Its
midpoint is O and its centre of mass is at C. Four axes pass 7 2
(a) PQ2 (b) PQ2
through A, B, O and C, all perpendicular to the length of the 2 7
rod. The moments of inertia of the rod about these axes are
2 5
IA, IB, IO and IC respectively. (c) PQ2 (d) PQ2
5 2
(a) IA > IB (b) IA< IB
(c) IO= IC (d) IO < IC 21. The moment of inertia of a rod of mass M and length L about
15. A stone of mass 4 kg is whirled in a horizontal circle of radius an axis passing through one edge and perpendicular to its
1m and makes 2 rev/sec. The moment of inertia of the stone length will be:
about the axis of rotation is-
ML2 ML2
(a) 64 kg × m2 (b) 4 kg × m2 (a) (b)
12 6
(c) 16 kg × m2 (d) 1 kg × m2
16. In an arrangement four particles, each of mass 2 units are ML2
(c) (d) ML2
situated at the coordinate points (3, 2, 0), (1, –1, 0), (0, 0, 0) 3
and (–1, 1, 0). The moment of inertia of this arrangement 22. Three thin uniform rods each of mass M and length L and
about the Z-axis will be-
placed along the three axis of a Cartesian coordinate system
(a) 8 units (b) 16 units
(c) 43 units (d) 34 units with one end of each rod at the origin. The M.I. of the system
about z-axis is:
17. A solid sphere and a hollow sphere of the same mass have
the same M.I. about their respective diameters. The ratio of ML2 2 ML2
their radii will be : (a) (b)
3 3
(a) 1 : 2 (b) 3: 5 ML2
(c) (d) ML2
(c) 5: 3 (d) 5 : 4 6
18. Three solid spheres of mass M and radius R are shown in 23. Four particles each of mass m are placed at the corners
the figure. The moment of inertia of the system about XX’ of a square of side length .The radius of gyration of the
axis wil be: system about an axis perpendicular to the square and passing
X
through centre is:
(a) (b)
2 2
(c) (d) 2
X'
2
, 24. The M.I. of a thin rod of length about the perpendicular
axis through its centre is I. The M.I. of the square structure
( ) (
29. Aforce of 2iˆ − 4 ˆj + 2kˆ Newton acts at a point 3iˆ + 2 ˆj − 4kˆ )
made by four such rods about a perpendicular axis to the metre from the origin. The magnitude of torque is:
plane and through the centre will be: (a) zero (b) 24.4 N-m
(a) 4 I (b) 8 I (c) 0.244 N-m (d) 2.444 N-m
30. Rate of change of angular momentum with respect to time
(c) 12 I (d) 16 I
is proportional to :
25. The moment of inertia of a ring of mass M and radius R (a) angular velocity (b) angular acceleration
about PQ axis will be: (c) moment of inertia (d) torque
D 31. When constant torque is acting on a body then:
P
(a) body maintain its state or moves in straight line with
M same velocity
(b) acquire linear acceleration
R (c) acquire angular acceleration
O O' (d) rotates with a constant angular velocity
32. If I = 50 kg-m2, then how much torque will be applied to
stop it in 10 sec. Its initial angular speed is 20 rad/sec:
(a) 100 N-m (b) 150 N-m
D' Q (c) 200 N-m (d) 250 N-m
MR 2 33. A particle is at a distance r from the axis of rotation. A given
(a) MR2 (b) torque τ produces some angular acceleration in it. If the mass
2
of the particle is doubled and its distance from the axis is
(c) 3/2MR2 (d) 2MR2 halved, the value of torque to produce the same angular
26. Four point masses (each of mass m) are arranged in the acceleration is:
X – Y plane the moment of inertia of this array of masses (a) τ/2 (b) τ (c) 2τ (d) 4τ
about Y-axis is ENERGY ANALYSIS
Y 34. A ring of radius r and mass m rotates about an axis passing
a (a,a)
through its centre and perpendicular to its plane with angular
a (2a,0) velocity ω. Its kinetic energy is
O a X
(0,0) 1 1 2 2
a (a) mrω (b) mrω2 (c) mr2ω2 (d) mr ω
(a,–a) 2 2
35. A rod of length L is hinged at one end. It is brought to a
(a) ma2 (b) 2ma2 horizontal position and released. The angular velocity of
(c) 4ma2 (d) 6ma2 the rod when it is in vertical position is
(a) 2 g / L (b) 3 g / L (c) g / 2 L (d) g/L
FIXED AXIS ROTATION , TOPPLING
36. Two bodies A and B having same angular momentum and
27. For a system to be in equilibrium, the torques acting on it
IA > IB, then the relation between (K.E.)A and (K.E.)B will be:
must balance. This is true only if the torques are taken about
(a) the centre of the system (a) (K.E.)A > (K.E.)B (b) (K.E.)A = (K.E.)B
(b) the centre of mass of the system (c) (K.E.)A < (K.E.)B (d) (K.E.)A ≤ (K.E.)B
(c) any point on the system
(d) any point on the system or outside it ANGULAR MOMENTUM
28. A rectangular block has a square base measuring a × a, and 37. A thin circular ring of mass M and radius r is rotating about
its height is h. It moves on a horizontal surface in a direction its axis with a constant angular velocity ω. Two objects,
perpendicular to one of the edges h being vertical. The each of mass m are attached gently to the opposite ends of a
coefficient of friction is µ. It will topple if
diameter of the ring. The wheel now rotates with an angular
h a velocity
(a) µ > (b) µ >
a h ωM ω ( M − 2m )
2a a (a) ( M + m) (b) ( M + 2m )
(c) µ > (d) µ >
h 2h ωM ω ( M + 2m )
(c) ( M + 2m ) (d)
M
3
, 38. A rotating table completes one rotation in 10 sec and its 46. One hollow and one solid cylinder of the same outer radius
moment of inertia is 100 kg-m2. A person of 50 kg mass rolls down on a rough inclined plane. The foot of the inclined
stands at the centre of the rotating table. If the person moves plane is reached by
2m. from the centre, the angular velocity of the rotating table (a) solid cylinder earlier
in rad/sec. will be: (b) hollow cylinder earlier
2π 20π (c) simultaneously
(a) (b)
30 30 (d) the heavier earlier irrespective of being solid or hollow
2π 47. If a solid sphere, disc and cylinder are allowed to roll down
(c) (d) 2 π
3 an inclined plane from the same height
39. A uniform heavy disc is rotating at constant angular velocity (a) cylinder will reach the bottom first
(ω) about a vertical axis through its centre O. Some wax is (b) disc will reach the bottom first
dropped gently on the disc. The angular velocity of the disc: (c) sphere will reach the bottom first
(a) does not change (b) increases (d) all will reach the bottom at the same time
(c) decreases (d) becomes zero 48. A solid homogeneous sphere is moving on a rough horizontal
40. A girl sits near the edge of a rotating circular platform. If surface, partly rolling and partly sliding. During this kind of
the girl moves from circumference towards the centre of the motion of the sphere
platform then the angular velocity of the platform will: (a) total kinetic energy is conserved
(a) decrease (b) increase (b) angular momentum of the sphere about the point of
(c) remain same (d) becomes zero contact with the plane is conserved
41. Two wheels P and Q are mounted on the same axle. The (c) only the rotational kinetic energy about the centre of
moment of inertia of P is 6 kg-m2 and it is rotating at 600 mass is conserved
rotations per minute and Q is at rest. If the two are joined (d) angular momentum about centre of mass is conversed
by means of a clutch then they combined and rotate at 400
rotations per minute. The moment of inertia of Q will be - 49. A ring of mass M is kept on a horizontal rough surface.
(a) 3 kg-m2 (b) 4 kg-m2 A force F is applied tangentially at its rim as shown. The
(c) 5 kg-m 2 (d) 8 kg-m2 coefficient of friction between the ring and the surface is µ.
Then
COMBINED ROTATION AND TRANSLATION F
42. If a spherical ball rolls on a table without slipping, the fraction
of its total kinetic energy associated with rotation is
(a) 3/5 (b) 2/7
f
(c) 2/5 (d) 3/7
(a) friction will act in the forward direction
43. The speed of a homogeneous solid sphere after rolling down
an inclined plane of vertical height h, from rest without (b) friction will act in the backward direction
sliding is (c) frictional force will not act
(a) gh (b) ( g / 5) gh (d) frictional force will be µ Mg.
50. A ring takes time t1 and t2 for sliding down and rolling down
(c) ( ) gh (d) ()gh
an inclined plane of length L respectively for reaching the
44. The rotational kinetic energy of a body is E. In the absence
bottom. The ratio of t1 and t2 is:
of external torque, if mass of the body is halved and radius
of gyration doubled, then its rotational kinetic energy will be: (a) 2:1 (b) 1 : 2 (c) 1 : 2 (d) 2 : 1
(a) 0.5 E (b) 0.25E 51. A ladder rests against a frictionless vertical wall, with its
(c) E (d) 2E upper end 6 m above the ground and the lower end 4 m away
45. A ring is rolling without slipping. Its energy of translation from the wall. The weight of the ladder is 500 N and its C.G.
is E. Its total kinetic energy will be: at 1/3rd distance from the lower end. Wall’s reaction will be,
(a) E (b) 2E (in Newton)
(c) 3E (d) 4E (a) 111 (b) 333 (c) 222 (d) 129
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