Rotational Kinematics & Rolling — Practice Questions

Free NEET Physics multiple-choice questions on Rotational Kinematics & Rolling. Attempt each question and reveal the answer with a full explanation.

A disc is rolling without slipping as shown. If the velocity of center of mass is v cm , then the velocity of point P at the top of the disc is: 2v cm v cm 2 v cm Zero A disc of mass M and radius R is rolling without slipping on a horizontal surface. The ratio of its translational kinetic energy to its total kinetic energy is: 2/3 1/3 1/2 3/4 If a spherical ball rolls on a table without slipping, the fraction of its total energy associated with rotation is: 2/7 2/5 3/5 5/7 The instantaneous power delivered by a torque to a body rotating with angular velocity is given by: / 1 2 2 2 A rigid body is rotating with an angular velocity about an axis. If the distance of a point from the axis is doubled, its linear velocity will: Double Become half Remain same Become four times A solid sphere and a hollow sphere of the same mass and same outer radius are released from the top of an inclined plane. The one that has greater acceleration is: Solid sphere Hollow sphere Both have same acceleration Depends on the coefficient of friction A disc of mass M and radius R is rolling without slipping. The ratio of rotational kinetic energy to the translational kinetic energy is: 1 : 2 2 : 1 1 : 1 2 : 3 An automobile engine develops 100 kW when rotating at a speed of 1800 rev/min . What torque does it deliver? 531 N m 350 N m 440 N m 628 N m A point P is at a distance r from the axis of rotation of a rigid body. If the angular velocity is and the position vector of the point is r , then the linear velocity v is given by: r r r r An engine brandishes a power of 60 W at 600 rpm . The torque delivered by the engine is: 30 rad/s is wrong units, correct is 30 N m 30 N m 60 N m 1 N m A solid cylinder of mass 2 kg and radius 0.2 m is free to rotate about its axis. A light string is wrapped around it and a force of 10 N is applied to the end of the string. The angular acceleration of the cylinder is: 50 rad/s 2 25 rad/s 2 5 rad/s 2 10 rad/s 2 A fly wheel rotates at a constant speed of 3000 rpm . The angle described by the shaft in 1 second is: 100 rad 50 rad 3000 rad 6000 rad A uniform disc of mass M and radius R rolls without slipping on a horizontal surface. What is the ratio of its rotational kinetic energy about its center of mass to its total kinetic energy? 1:3 1:2 2:3 1:4 A rigid body is in pure rotation about a fixed axis. The linear velocity of a point at a distance r from the axis is v . The tangential acceleration of the point is a t . The angular acceleration is given by: = a t / r = v / r = a t r = v 2 / r A wheel of moment of inertia 2 kg m 2 is rotating at an angular speed of 20 rad/s . The torque required to stop it in 4 seconds is: 10 N m 40 N m 5 N m 2.5 N m A constant torque of 50 N m is applied to a body of moment of inertia 10 kg m 2 . The angular velocity of the body after 2 seconds , starting from rest, is: 10 rad/s 5 rad/s 20 rad/s 25 rad/s 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. Which one will reach the bottom first? Solid cylinder Hollow cylinder Both will reach at the same time Depends on the angle of inclination A solid cylinder of mass 2 kg and radius 50 cm is free to rotate about its axis. A string is wound around the cylinder and a constant pull of 10 N is applied. The angular acceleration of the cylinder is: 20 rad/s 2 10 rad/s 2 5 rad/s 2 25 rad/s 2 A spherical shell of 1 kg mass and radius R is rolling with angular speed on horizontal plane. The magnitude of angular momentum of the shell about the origin O is L . The relationship between v and is v = R . What is the total kinetic energy of the shell? 5 6 mv 2 1 2 mv 2 2 3 mv 2 1 3 mv 2 A solid sphere is rolling without slipping on a horizontal surface. The ratio of its translational kinetic energy to its rotational kinetic energy is: 5 : 2 2 : 5 7 : 2 2 : 7 A hollow cylinder of mass M and radius R rolls down an inclined plane of inclination without slipping. The acceleration of the cylinder is: 1 2 g g 2 3 g 3 4 g A point P is at the top of a wheel of radius R rolling without slipping on a horizontal surface. If the speed of the center of the wheel is v , the magnitude of the velocity of point P relative to the ground is: 2v v 2 v 4v A uniform cylinder of radius R is rolling without slipping. The ratio of the velocity of the top-most point to the velocity of the center of mass is: 2:1 1:1 2 :1 4:1 The instantaneous axis of rotation for a wheel of radius R rolling without slipping on a horizontal surface is located at: The point of contact with the ground The center of the wheel The top point of the wheel Infinity The power delivered by a torque = (2 i + 3 j ) N m to a body rotating with angular velocity = (4 i + 2 j ) rad/s is: 14 W 10 W 8 W 6 W A constant torque of 1000 N m turns a wheel of moment of inertia 200 kg m 2 about an axis through its center. Its angular velocity after 3 seconds is: 15 rad/s 10 rad/s 5 rad/s 20 rad/s A pulley of moment of inertia I and radius R is rotated by a string under a constant tension T . The angular acceleration produced is: TR/I T/I I/(TR) TR 2/I A solid sphere is rolling without slipping on a horizontal surface. The ratio of its translational kinetic energy to its rotational kinetic energy is: 5:2 2:5 7:2 2:7 A disk 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? Sphere Disk Both reach at the same time Depends on their masses A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its center of mass has speed of 20 cm/s . How much work is needed to stop it? 3 J 1 J 30 kJ 2 J A solid sphere, a thin hollow sphere, a solid cylinder and a thin hollow cylinder (all having same mass and radius) are rolling down an inclined plane without slipping. The one that will reach the bottom first is: Solid sphere Solid cylinder Hollow sphere Hollow cylinder The ratio of rotational kinetic energy to the total kinetic energy for a solid sphere in pure rolling is: 2 : 7 2 : 5 5 : 7 1 : 2 A uniform rod of length L and mass M is free to rotate in a vertical plane about a hinge at one end. The rod is released from rest in the horizontal position. The initial angular acceleration of the rod is: 3g 2L g L 2g 3L 3g L A particle moves in a circle of radius 0.5 m with linear speed 2 m/s . The angular speed is: 4 rad/s 1 rad/s 2 rad/s 0.25 rad/s A solid sphere is in pure rolling motion. In rolling motion, a body possesses translational kinetic energy ( K t ) as well as rotational kinetic energy ( K r ) simultaneously. The ratio K t : (K t + K r) for the sphere is: 5 : 7 2 : 5 2 : 7 10 : 7 A disc of radius R and mass M is rolling without slipping on a horizontal surface with velocity v . It then rolls up an inclined plane to a maximum height h . The value of h is: 3v 2 4g v 2 2g v 2 g 2v 2 3g 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 ? 25 rad/s 2 0.25 rad/s 2 5 rad/s 2 0.5 rad/s 2 The ratio of the acceleration for a solid sphere (mass m and radius R ) rolling down an incline of angle without slipping and slipping down the same incline without rolling is: 5:7 2:3 2:5 7:5 A solid sphere, a solid cylinder and a circular disc, all having the same mass and radius, are allowed to roll down an inclined plane without slipping from the same height. Which of the following statements is correct? The sphere reaches the bottom with the maximum velocity. The cylinder reaches the bottom with the maximum velocity. The disc reaches the bottom with the maximum velocity. All reach the bottom with the same velocity. A solid sphere rolls down an inclined plane without slipping. The acceleration of its center of mass is a . If the same sphere slides down the same smooth inclined plane, its acceleration will be a' . The ratio a/a' is: 5/7 2/7 3/5 1/2 A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its center of mass is k . If the radius of the ball is R , then the fraction of total kinetic energy associated with its translational motion is: R 2 R 2 + k 2 k 2 R 2 + k 2 R 2 + k 2 R 2 k 2 R 2 A solid cylinder of mass M and radius R rolls down an inclined plane of height h without slipping. The speed of its center of mass when it reaches the bottom is: 4gh 3 2gh 3gh 4 gh A cylinder of mass 10 kg and radius 15 cm is rolling without slipping on a plane of inclination 30 . The co-efficient of static friction s should be at least: 1 3 3 1 2 3 3 2 1 3 A uniform rod of length L and mass M is pivoted at one end. It is held horizontal and released. The angular acceleration of the rod the moment it is released is: 3g 2L g L 2g 3L 3g L The instantaneous angular position of a point on a rotating wheel is given by the equation (t) = 2t 3 - 6t 2 . The torque on the wheel becomes zero at t equal to: 1 s 0.5 s 2 s 2.5 s A wheel starting from rest is uniformily accelerated at 4 rad/s 2 for 10 s . It is then allowed to rotate at the velocity acquired and finally brought to rest in next 10 s . Total angle rotated by the wheel is: 800 rad 600 rad 400 rad 200 rad A solid sphere, a disc and a ring, all of the same mass and radius, roll down an inclined plane without slipping. The one that has the minimum velocity at the bottom is: Ring Disc Solid sphere All have the same velocity A solid sphere rolls down an inclined plane of height h without slipping. The speed of the sphere at the bottom of the plane is: 10gh 7 2gh 4gh 3 5gh 3 The ratio of the acceleration of a hollow cylinder (rolling without slipping) to a solid cylinder (rolling without slipping) down the same inclined plane is: 3:4 4:3 1:2 2:3 A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. If their translational kinetic energies are equal, then the ratio of their total kinetic energies is: 14 : 15 2 : 5 5 : 2 15 : 14 The speed of a point on the rim of a wheel rolling without slipping on a horizontal surface, relative to the ground, when the point is at the same height as the center, is: 2 v cm v cm 2v cm Zero A uniform thin rod of length L is pivoted at one end and held vertically. If it is allowed to fall, the linear velocity of its free end when it reaches the horizontal position is: 3gL gL 2gL 3gL 2 A solid sphere and a solid cylinder of same mass and radius are released from the top of an inclined plane. The ratio of their accelerations a sphere : a cylinder is: 15 : 14 14 : 15 5 : 4 4 : 5 If the rotational kinetic energy of a body is 50 % of its total kinetic energy in pure rolling, the body must be a: Hollow cylinder Solid cylinder Solid sphere Hollow sphere A solid cylinder of mass M and radius R is rolling down an incline. If the friction is sufficient to prevent slipping, what is the work done by friction as it moves a distance d along the incline? Zero Mgd 1 3 Mgd Mgd A solid cylinder of mass M and radius R is rolling without slipping on a horizontal plane with speed v . The total kinetic energy of the cylinder is: 3 4 Mv 2 1 2 Mv 2 1 4 Mv 2 Mv 2 A solid sphere is rolling without slipping. The percentage of its total kinetic energy that is translational is: 71.4 % 60 % 28.6 % 40 % A solid sphere, a solid cylinder and a hollow cylinder are rolling down an inclined plane without slipping. They all have the same mass and radius. The ratio of their accelerations a sphere : a cylinder : a hollow cyl is: 14 : 12 : 10 10 : 12 : 14 5 : 4 : 3 15 : 10 : 8 A solid sphere is rolling on a horizontal surface without slipping. If the velocity of its center of mass is v , then the velocity of a point on its surface at the same horizontal level as the center of mass is: 2 v v 2v v/ 2 A uniform rod of length L is pivoted at one end and held vertically. It is released from rest and allowed to fall. Its angular velocity when it makes an angle with the vertical is: 3g L (1- ) 2g L (1- ) 3g L g L For a body rolling without slipping on a horizontal surface, the friction at the point of contact: is zero if the velocity is constant always acts in the direction of motion always acts opposite to the direction of motion is equal to s N always A disc of mass M and radius R rolls without slipping on a horizontal surface. If its translational kinetic energy is K , then its total kinetic energy is: 3 2 K 2 K 5 2 K 4 3 K A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at a rate of 3 rpm . The torque required to stop after 2 revolutions is: 2 10 -6 N m 2 10 -3 N m 12 10 -4 N m 2 10 6 N m A solid sphere of mass M and radius R is pulled by a horizontal force F acting through the center. If it rolls without slipping, the acceleration of the center of mass is: 5F 7M 2F 3M 3F 5M F M A sphere rolls down on an inclined plane of inclination . What is the minimum coefficient of friction required so that it rolls without slipping? 2 7 2 5 5 7 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 center. 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: 8.0 7.0 6.0 3.0 A wheel has a moment of inertia of 2 kg m 2 . It is rotating at 50 rad/s . To stop it in 5 seconds , the constant torque required is: 20 N m 10 N m 40 N m 5 N m A solid sphere is rolling without slipping on a horizontal surface. The velocity of the center of mass is v . What is the velocity of a point on the sphere at the same vertical height as the center of mass? 2 v v 2v 3 v A uniform rod of length L is balanced on a sharp edge. If the support is suddenly removed, and the rod starts falling, the acceleration of the center of mass of the rod at the instant it becomes horizontal is (given it was pivoted at one end): 3g 4 g 2 g 3g 2 A solid cylinder of mass M and radius R is rolling down an incline of angle without slipping. The magnitude of the friction force acting on it is: 1 3 Mg 1 2 Mg Mg 2 3 Mg A spherical shell of mass M and radius R rolls without slipping down an incline of angle . The friction force f acting on the shell is: 2 5 Mg 2 3 Mg 3 5 Mg 1 3 Mg A solid sphere is rolling on a horizontal surface. What fraction of its total kinetic energy is rotational kinetic energy? 2/7 2/5 3/7 5/7 The ratio of rotational kinetic energy to the total kinetic energy for a hollow sphere rolling without slipping is: 2/5 3/5 2/3 1/2