Rotational Motion · Physics · NEET
MCQ (Single Correct Answer)
1
The radius of gyration of a solid sphere of mass $$5 \mathrm{~kg}$$ about $$X Y$$ is $$5 \mathrm{~m}$$ as shown in figure. The radius of the sphere is $$\frac{5 x}{\sqrt{7}} \mathrm{~m}$$, then the value of $x$ is:
NEET 2024 (Re-Examination)
2
A bob is whirled in a horizontal plane by means of a string with an initial speed of $$\omega \mathrm{~rpm}$$. The tension in the string is $$T$$. If speed becomes $$2 \omega$$ while keeping the same radius, the tension in the string becomes:
NEET 2024
3
The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is $$2400 \mathrm{~g} \mathrm{~cm}^2$$. The length of the $$400 \mathrm{~g}$$ rod is nearly:
NEET 2024
4
A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is $$v$$ in the direction shown, which one of the following options is correct ($$P$$ and $$Q$$ are any highest and lowest points on the wheel, respectively)?
NEET 2024
5
A constant torque of $$100 \mathrm{~N} \mathrm{~m}$$ turns a wheel of moment of inertia $$300 \mathrm{~kg} \mathrm{~m}^2$$ about an axis passing through its centre. Starting from rest, its angular velocity after $$3 \mathrm{~s}$$ is :-
NEET 2023 Manipur
6
The ratio of radius of gyration of a solid sphere of mass $$M$$ and radius $$R$$ about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is :-
NEET 2023
7
The angular acceleration of a body, moving along the circumference of a circle, is :
NEET 2023
8
An energy of 484 J is spent in increasing the speed of a flywheel from 60 rpm to 360 rpm. The moment of inertia of the flywheel is :
NEET 2022 Phase 2
9
The angular speed of a fly wheel moving with uniform angular acceleration changes from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration in rad/s2 is
NEET 2022 Phase 1
10
The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is
NEET 2022 Phase 1
11
From a circular ring of mass 'M' and radius 'R' an arc corresponding to a 90$$^\circ$$ sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the center of the ring and perpendicular to the plane of the ring is 'K' times 'MR2'. Then the value of 'K' is :
NEET 2021
12
A uniform rod of length 200 cm and mass 500 g is balanced on a wedge placed at 40 cm mark. A mass of 2 kg is suspended from the rod at 20 cm and another unknown mass 'm' is suspended from the rod at 160 cm mark as shown in the figure. Find the value of 'm' such that the rod is in equilibrium. (g = 10 m/s2)
NEET 2021
13
Find the torque about the origin when a force of 3 $$\hat j$$
N acts on a particle whose position vector is 2 $$\hat k$$ m.
NEET 2020 Phase 1
14
A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after 2$$\pi $$ revolutions is :
NEET 2019
15
Two particles A and B are moving in uniform circular motion in concentric circles of radii rA and rB with speed vA and vB respecitively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be :
NEET 2019
16
A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it?
NEET 2019
17
A solid sphere is in rolling motion. In rolling
motion a body possesses translational kinetic
energy (Kt) as well as rotational kinetic energy
(Kr) simultaneously. The ratio Kt
: (Kt + Kr)
for the sphere is
NEET 2018
18
A solid sphere is rotating freely about its
symmetry axis in free space. The radius of
the sphere is increased keeping its mass same.
Which of the following physical quantities
would remain constant for the sphere?
NEET 2018
19
Three objects, A : (a solid sphere), B : (a thin
circular disk) and C : (a circular ring), each
have the same mass M and radius R. They
all spin with the same angular speed $$\omega $$ about
their own symmetry axes. The amounts of
work (W) required to bring them to rest, would
satisfy the relation
NEET 2018
20
The moment of the force, $$\overrightarrow F = 4\widehat i + 5\widehat j - 6\widehat k$$ at
(2, 0, –3), about the point (2, –2, –2), is given by
(2, 0, –3), about the point (2, –2, –2), is given by
NEET 2018
21
Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities $${\omega _1}$$ and $${\omega _2}$$. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is
NEET 2017
22
A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?
NEET 2017
23
Two rotating bodies A and B of masses m and 2m with moments of inertia $${I_A}$$ and $${I_B}$$ ($${I_B}$$ > $${I_A}$$) have equal kinetic energy of rotation. If LA and LB be their angular momenta respectively, then
NEET 2016 Phase 2
24
A light rod of length $$l$$ has two masses m1 and m2 attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is
NEET 2016 Phase 2
25
A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation (Esphere / Ecylinder) will be
NEET 2016 Phase 2
26
A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of 2.0 rad s$$-$$2. Its net acceleration in m s$$-$$2 at the end of 2.0 s is approximately
NEET 2016 Phase 1
27
From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre?
NEET 2016 Phase 1
28
A disc and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?
NEET 2016 Phase 1
29
A force $$\overrightarrow F = \alpha \widehat i + 3\widehat j + 6\widehat k$$ is acting at a point $$\overrightarrow r = 2\widehat i - 6\widehat j - 12\widehat k$$. The value of $$\alpha $$ for which angular momentum about origin is conserved is
AIPMT 2015
30
Point masses m1 and m2 are placed at the opposite ends of a rigid rod of length L, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity $$\omega $$0 is minimum, is given by
AIPMT 2015
31
An automobile moves on a road with a speed of 54 km h$$-$$1. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m2. If the vehicle is brought to rest in 15 s, the magnitude of average torque transmitted by its brakes to the wheel is
AIPMT 2015
32
Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX' which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three spherical shells about XX' axis is
AIPMT 2015 Cancelled Paper
33
A mass m moves in a circle on a smooth horizontal plane with velocity v0 at a radius R0. The mass is attached to a string which passes through a smooth hole in the plane as shown. the tension in the string is increased gradually and finally m moves in a circle of radius $${{{R_0}} \over 2}$$.
The final value of the kinetic energy is
The final value of the kinetic energy is
AIPMT 2015 Cancelled Paper
34
A rod of weight W is supported by two parallel knife edges A and B and is in equilibrium in a horizontal position. The knives are at a distance d from each other. The centre of mass of the rod is at distance x from A. The normal reaction on A is
AIPMT 2015 Cancelled Paper
35
The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle $$\theta $$ without slipping and slipping down the incline without rolling is
AIPMT 2014
36
A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s$$-$$2 is
AIPMT 2014
37
The ratio of radii of gyration of a circular ring and a circular disc, of the same mass and radius, about an axis passing through their centres and perpendicular to their planes are
NEET 2013 (Karnataka)
38
Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D1 has 2 kg mass and 0.2 m radius and initial angular velocity of 50 rad s$$-$$1. Disc D2 has 4 kg mass, 0.1 m radius and initial angular velocity of 200 rad s$$-$$1. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad s$$-$$1) of the system is
NEET 2013 (Karnataka)
39
A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is
NEET 2013
40
A small object of uniform density rolls up a curved surface with an initial velocity 'v'. It reaches upto a maximum height of $${{3{v^2}} \over {4g}}$$ with respect to the initial position. The object is
NEET 2013
41
The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through
AIPMT 2012 Mains
42
A car of mass m is moving on a level circular track of radius R. If $$\mu $$s represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by
AIPMT 2012 Mains
43
A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia about the axle is 200 kg m2. It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1 ms$$-$$1 relative to the ground. Time taken by the man to complete one revolution is
AIPMT 2012 Mains
44
ABC is an equilateral triangle with O as its centre. $${\overrightarrow F _1},{\overrightarrow F _2}$$ and $${\overrightarrow F _3}$$ represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero then magnitude of $${\overrightarrow F _3}$$ is
AIPMT 2012 Prelims
45
A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45o, the speed of the car is
AIPMT 2012 Prelims
46
When a mass is rotating in a plane about a fixed point, its angular momentum is directed along
AIPMT 2012 Prelims
47
A small mass attached to a string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will
AIPMT 2011 Mains
48
The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is $$I$$0. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is
AIPMT 2011 Prelims
49
The instantaneous angular position of a point on a rotating wheel is given by the equation $$\theta \left( t \right) = 2{t^3} - 6{t^2}$$
The torque on the wheel becomes zero at
The torque on the wheel becomes zero at
AIPMT 2011 Prelims
50
A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity $$\omega $$. Two objects each of msass m are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by
AIPMT 2010 Mains
51
A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?
AIPMT 2010 Mains
52
From a circular disc of radius R and mass 9M, a small disc of mass M and radius $${R \over 3}$$ is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is
AIPMT 2010 Mains
53
A gramophone record is revolving with an angular velocity $$\omega $$. A coin is placed at a distance r from the centre of the record. The static coefficient of friction is $$\mu $$. The coin will revolve with the record if
AIPMT 2010 Prelims
54
A circular disk of moment of inertia $${I_t}$$ is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed $${\omega _i}$$. Another disk of moment of inertia $${I_b}$$ is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed $$\omega $$. The energy lost by the initially rotating disc to friction is
AIPMT 2010 Prelims
55
If $$\overrightarrow F $$ is the force acting on a particle having position vector $$\overrightarrow r $$ and $$\overrightarrow \tau $$ be the torque of this force about the origin, then
AIPMT 2009
56
Four identical thin rods each of mass M and length $$l$$, form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is
AIPMT 2009
57
A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity $$\omega $$. If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity
AIPMT 2009
58
The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is
AIPMT 2008
59
A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is 90o. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is
AIPMT 2008
60
A wheel has angular acceleration of 3.0 rad/sec2 and an initial angular speed of 2.00 rad/sec. In a time of 2 sec it has rotated through an angle (in radian) of
AIPMT 2007
61
A particle of mass m moves in the XY plane with a velocity v along the straight line AB. If the angular momentum of the particle with respect to origin O is LA when it is at A and LB when it is at B, then
AIPMT 2007
62
A uniform rod AB of length $$l$$ and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is ml2/3, the initial angular acceleration of the rod will be
AIPMT 2007
63
A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $$\omega $$. The force exerted by the liquid at the other end is
AIPMT 2006
64
The moment of inertia of a uniform circular disc of radius R and mass M about an axis touching the disc at its diameter and normal to the disc
AIPMT 2006
65
A uniform rod AB of length $$l$$ and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is ml2/3, the initial angular acceleration of the rod will be
AIPMT 2006
66
Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular velocity will be in the ratio
AIPMT 2005
67
A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle $$\theta $$. The frictional force
AIPMT 2005
68
The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge of the disc and normal to the disc is
AIPMT 2005
69
The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axes in the plane of the ring is
AIPMT 2004
70
A round disc of moment of inertia $$I$$2 about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia $$I$$1 rotating with an angular velocity $$\omega $$ about the same axis. The final angular velocity of the combination of discs is
AIPMT 2004
71
A wheel having moment of inertia 2 kg m2 about its vertical axis, rotates at the rate of 60 rpm about this axis. The torque which can stop the wheel's rotation in one minute would be
AIPMT 2004
72
Three particles, each of mass m gram, are situated at the vertices of an equilateral triangle ABC of side $$l$$ cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram-cm2 units will be
AIPMT 2004
73
A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity $$\omega $$. Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be :
AIPMT 2003
74
A solid cylinder of mass M and radius R rolls without slipping down an inclined plane of length L and height h. What is the speed of its centre of mass when the cylinder reaches its bottom ?
AIPMT 2003
75
A stone is tied to a string of length $$l$$ and is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change in velocity as it reaches a position where the string is horizontal (g being acceleration due to gravity) is
AIPMT 2003
76
A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R. then the fraction of total energy associated with its rotational energy will be
AIPMT 2003
77
A point P consider at contact point of a wheel on ground which rolls on ground without slipping then value of displacement of point P when wheel completes half of rotation (if radius of wheel is 1 m)
AIPMT 2002
78
A circular disc is to be made by using iron and aluminium so that it acquired maximum moment of inertia about geometrical axis. It is possible with
AIPMT 2002
79
A disc is rotating with angular speed $$\omega $$. If a child sits on it, what is conserved
AIPMT 2002
80
A solid sphere of radius R is placed on smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of centre of mass, which is correct ?
AIPMT 2002
81
As shown in the figure at point O a mass is performing vertical circular motion. The average velocity of the particle is increased, then at which point will the string break
AIPMT 2000
82
For a hollow cylinder and a solid cylinder rolling without slipping on an inclined plane, then which of these reaches earlier
AIPMT 2000
83
For the adjoining diagram, the correct relation between I1, I2, and I3 is, (I-moment of inertia)
AIPMT 2000