Angular Momentum & Conservation — Practice Questions

Free NEET Physics multiple-choice questions on Angular Momentum & Conservation. Attempt each question and reveal the answer with a full explanation.

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? Angular momentum Moment of inertia Angular velocity Rotational kinetic energy A particle of mass m moves along a straight line y = c with a constant velocity v . Its angular momentum about the origin: Remains constant Increases with time Decreases with time Is zero A thin circular ring of mass M and radius R is rotating about its central axis with angular velocity . If the mass of the ring is kept constant but the radius is doubled, then the new angular velocity will be: 4 2 2 4 A solid sphere is rotating about its diameter. If the kinetic energy of rotation is E , then the angular momentum is: 4IE 5 is incorrect, correct is 2IE 2IE 1 2 IE 2IE If the angular momentum of a body is increased by 50 % , its kinetic energy of rotation will increase by: 125 % 50 % 100 % 225 % A disc is rotating with angular velocity . A child sits on it. What is conserved? Angular momentum Linear momentum Kinetic energy Moment of inertia The angular momentum of a system of particles is conserved: When no external torque acts on the system When no external force acts on the system When net work done by external forces is zero When the system is in equilibrium If the net external torque acting on a system is zero, which of the following remains constant? Angular momentum Linear momentum Rotational kinetic energy Moment of inertia A particle is moving in a circular path with constant tangential acceleration. If the angular momentum of the particle about the center of the circle is L , then the torque acting on it is related to L as: = dL dt = L t = L t = 0 If the radius of the earth contracts to half of its present value without change in its mass, what will be the new duration of the day? 6 hours 12 hours 48 hours 3 hours A disc of mass M and radius R is rotating about its center with angular velocity 0 . If the radius of the disc is doubled without changing its mass, the new angular velocity will be: 0/4 0/2 2 0 0 Two bodies with moments of inertia I 1 and I 2 ( I 1 > I 2 ) have equal angular momenta. If E 1 and E 2 are their rotational kinetic energies, then: E 2 > E 1 E 1 > E 2 E 1 = E 2 E 1 E 2 = 1 When a mass is rotating in a plane about a fixed point, its angular momentum is directed along: The axis of rotation The radius The tangent to the orbit A line inclined at 45 to the plane of rotation If the kinetic energy of a rotating body is E and its angular momentum is L , then its moment of inertia I is given by: L 2 2E L 2 E 2E L 2 E L 2 A planet moves around the sun in an elliptical orbit. Its angular momentum L is: Constant at all points of the orbit Maximum at perihelion Maximum at aphelion Varies with the distance from the sun The power P required to maintain a rotor at a constant angular velocity against a resistive torque r = k is: k 2 k 1 2 k 2 k 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- 1 2 MR 2 7 2 MR 2 3 2 MR 2 MR 2 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 ω about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation W B > W A > W C W A > W B > W C W C > W B > W A W A > W C > W B From a circular ring of mass 'M' and radius 'R' an arc corresponding to a 90 sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is 'K' times ' MR 2 '. Then the value of 'K' is 7 8 1 4 1 8 3 4 The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is 2400 g cm 2 . The length of the 400 g rod is nearly: 8.5 cm 17.5 cm 20.7 cm 72.0 cm A force F = i + 3 j + 6 k is acting at a point r = 2 i - 6 j - 12 k . The value of for which angular momentum is conserved about the origin is: -1 1 2 0 A particle of mass m moves in the XY plane with a velocity v along the straight line y = b . The angular momentum of the particle about the origin is: mvb (constant) mvb (varying) Zero mvx The angular momentum of a system of particles is not conserved when: A non-zero external torque acts on the system A non-zero external force acts on the system Internal forces are dissipative The center of mass is accelerating If the earth were to suddenly contract to half of its present radius (without any change in its mass), the duration of the new day will be: 6 hours 12 hours 3 hours 48 hours A thin circular ring of mass M and radius R is rotating about its axis 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 an angular velocity: M M+2m (M-2m) M+2m M M+m (M+2m) M An object of mass m is moving with a constant velocity v in the xy -plane along the line y = x + 4 . The angular momentum of the object about the origin is: 2 2 mv 4mv Zero Dependent on x The angular momentum of a body with moment of inertia I and angular velocity is L . If its kinetic energy of rotation is doubled and angular velocity is halved, the new angular momentum will be: 4L 2L L/2 8L A small mass m is attached to a string of length l and is being whirled in a horizontal circle with a constant angular velocity . If the string is suddenly shortened to l/2 while keeping angular momentum constant, the new kinetic energy is: 4 times the initial 2 times the initial Same as initial 1/4 times the initial A particle of mass m is moving with constant velocity v along a line y = x + a . The magnitude of its angular momentum about the origin is: mva 2 mva 2 mva 2mva A particle of mass m is moving in a plane along a straight line with constant velocity v . Which of the following statements about the angular momentum L of the particle about the origin is true? L remains constant L increases with time L decreases with time L is zero if the line passes through the origin A disc of mass M and radius R is rotating about its center with angular velocity . A small insect of mass m lands on the edge of the disc. The new angular velocity of the disc is: M M + 2m M + 2m M M M + m M + m M The angular momentum of a planet of mass M moving in a circular orbit of radius r around the Sun is L . If the radius of the orbit is increased to 4r , the new angular momentum (assuming it still follows a circular orbit) will be: 2L 4L L 2 L The angular momentum of a satellite of mass m revolving round the earth in a circular orbit of radius r is proportional to: r 1/2 r r 3/2 r 2 If the angular momentum of a body is L and its moment of inertia is I , its rotational kinetic energy is: L 2/2I L 2/I I 2/2L L/2I 2 A uniform rod of mass M and length L is pivoted at its center and is free to rotate in a horizontal plane. A small ball of mass m moving with speed v perpendicularly strikes one end of the rod and sticks to it. The angular velocity of the system just after the collision is: 6mv (M + 6m)L mv (M + 3m)L 3mv (M + 3m)L 2mv (M + 2m)L A person of mass M stands at the center of a rotating turntable of radius R and moment of inertia I . The turntable is rotating with angular velocity 0 . If the person walks to the edge of the turntable, the new angular velocity is: I 0 I + MR 2 (I + MR 2) 0 I I 0 MR 2 0 A uniform disc of mass M and radius R is rotating about its axis with angular velocity . Another disc of same radius but mass M/2 is placed gently on the first disc coaxially. The new angular velocity of the system will be: 2 /3 /2 3 /4 4 /5 A particle of mass m is moving with a constant velocity v along a line y = x + a . The magnitude of its angular momentum about the origin is: mva 2 mva 2 mva 2mva A disc is rotating with an angular velocity . If a second identical disc is gently placed coaxially on the first disc, the fraction of the initial kinetic energy dissipated as heat is: 1/2 1/4 1/3 2/3 A disc of mass M and radius R is rotating with angular velocity 0 . Another disc of mass M and radius R/2 is placed gently on it coaxially. The new angular velocity of the system is: 4 5 0 2 3 0 1 2 0 3 4 0 A uniform rod of length L and mass M is lying on a smooth horizontal surface. It is struck by a particle of mass m moving with velocity v perpendicular to the rod at a distance L/4 from the center. If the particle stops after collision, the angular velocity of the rod is: 3mv ML 12mv ML 6mv ML mv ML A circular disc of mass M and radius R is rotating about its axis with angular speed 1 . If another identical disc is placed gently on the first disc coaxially, the work done by the friction between the two discs is: - 1 8 MR 2 1 2 1 4 MR 2 1 2 - 1 4 MR 2 1 2 1 2 MR 2 1 2 The angular momentum of a particle performing uniform circular motion of radius r is L . If its angular frequency is doubled and its kinetic energy is halved, then the new angular momentum is: L 4 L 2 2L 4L A solid cylinder of mass M and radius R is rolling without slipping on a horizontal surface. Its angular momentum about the point of contact with the ground is: 3 2 M R v 1 2 M R v M R v 5 2 M R v A particle of mass m is moving with a constant velocity v along a line parallel to the x -axis at a distance h from it. The magnitude of its angular momentum about the origin is: mvh mvx Zero mv x 2+h 2 A disc of moment of inertia I 1 is rotating with angular velocity 1 . It is coupled coaxially with a second disc of moment of inertia I 2 which is initially at rest. The final angular velocity of the system is: I 1 1 I 1 + I 2 I 1 1 I 2 (I 1 + I 2) 1 I 1 I 2 1 I 1 + I 2 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 is:- MR 2 2 5 MR 2 3 2 MR 2 1 2 MR 2 A uniform rod AB of length , 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 m 2 3 , the initial angular acceleration of the rod will be mg 2 3 2 g 3g 2 2g 3 . Four identical thin rods each of mass M and length l , from a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is : 1 3 Ml 2 4 3 Ml 2 2 3 Ml 2 13 3 Ml 2 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 3g 2L g L 2g L 2g 3L 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 ? 15 ,MR 2/32 13 ,MR 2/32 11 ,MR 2/32 9 ,MR 2/32 A thin uniform rod of mass ‘M’ and length ‘L’ is rotating about a perpendicular axis passing through its centre with a constant angular velocity ‘ ’. Two objects each of mass M 3 are attached gently to the two ends of the rod. The rod will now rotate with an angular velocity of : 1 3 1 7 1 6 1 2 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 2 : 1 4 : 1 1 : 2 2 : 1 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 3 : 5 5 : 3 2 : 5 5 : 2 A thin wire of length ‘L’ and linear mass density ‘m’ is bent into a circular ring (in x-y plane) with centre ‘C’ as shown in figure. The moment of inertia of the ring about an axis yy' will be : 3mL 3 8 3mL 2 8 2 3mL 3 8 2 3mL 2 8 A small object of mass m is attached to a light string which passes through a hollow tube. The object is set into rotation in a circle of radius r 1 with angular speed 1 . The string is then pulled down, shortening the radius to r 2 . The new angular speed 2 is: 1(r 1/r 2) 2 1(r 1/r 2) 1(r 2/r 1) 2 1(r 2/r 1) Two discs of same moment of inertia rotating about their regular axes passing through center and perpendicular to the plane of disc with angular velocities 1 and 2 . They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is: 1 4 I( 1 - 2) 2 1 2 I( 1 - 2) 2 I( 1 - 2) 2 1 8 I( 1 - 2) 2 A uniform rod of length L is free to rotate in a vertical plane about a fixed horizontal axis through one end. The rod is allowed to fall from its vertical position. The angular velocity of the rod when it has turned through an angle is: 3g L (1- ) 2g L (1- ) 3g L g L (1- ) A circular ring of mass M and radius R is rotating about its axis with angular velocity . Two particles each of mass m are attached gently to the ring at the ends of a diameter. The loss in rotational kinetic energy is: m M 2 R 2 M + 2m m M 2 R 2 M + m 2m M 2 R 2 M + 2m m M 2 R 2 2(M + 2m) A uniform rod of length L and mass M is lying on a smooth horizontal table. A particle of mass m strikes the rod perpendicularly at one end and stops. If the velocity of the particle was v , the angular velocity of the rod just after the collision is: 6mv/ML 3mv/ML mv/ML 12mv/ML A thin uniform rod of length L and mass M is swinging in a vertical plane about a horizontal axis through one end. If the maximum angular velocity is , the maximum height to which the center of mass rises from its lowest position is: L 2 2 6g L 2 2 3g L 2 2 2g L 2 2 4g A particle of mass m is projected with velocity v at an angle of 60 with the horizontal. The magnitude of the angular momentum of the particle about the point of projection when it is at the highest point of its trajectory is: 3 mv 3 8g mv 3 4g 3 mv 3 2g 3mv 3 8g A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y -axis is: 7 64 7 8 7 40 7 57 A thin horizontal disc is rotating about a vertical axis passing through its fixed centre O . Its angular momentum is L A and L B computed about points A and B , respectively, with OB=2 OA . The value of L A L B is: 1 4 1 2 1 2 A man stands on a rotating platform, with his arms stretched horizontally holding a 5 kg weight in each hand. The angular speed of the platform is 30 rpm . The man then pulls his arms close to his body. The new angular speed will be: More than 30 rpm Less than 30 rpm 30 rpm Zero 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 momenta will be in the ratio: 1 : 2 2 : 1 1 : 2 2 : 1 A solid sphere is rotating about its diameter. If the radius is doubled keeping the mass constant, the new angular velocity ' in terms of the initial angular velocity will be: /4 /2 4 2