Rotational Motion — practice questions

184 curated practice questions from Rotational Motion (Physics JEE Advanced, NTA Exams) — 183 hard, 1 medium. Every question includes the final answer free; step-by-step worked solutions with a free account.

• A particle of mass m is attached to a light string which passes through a hollow tube. The tube is held by one hand and…
• Two identical particles, A and B, are attached to a string of length 2 l , A to middle and B to one of the ends. The…
• A cubical block of edge a is moving with velocity v on a horizontal smooth plane as shown in figure. It hits a ridge at…
• A projectile is projected at certain angle. The angular momentum about origin will
• Statement–1: A ring moving down on a smooth inclined plane will be in slipping motion. Statement–2: Work done by…
• A horizontal disc rotates freely about a vertical axis through its centre. A ring, having the same mass and radius as…
• A cricket mat of mass 50 kg is rolled loosely in the form of a cylinder of radius 2m. Now again it is rolled tightly so…
• A solid sphere radius 1 m and mass 2 kg is rolling with a linear speed of 2 m/s. What is speed of point A
• With what minimum speed v must a small ball should be pushed inside a smooth vertical tube from a height h so that it…
• Each pulley shown in the given figure below has radius r and moment of inertia I. The acceleration of the block is
• A ring (R), a disc (D), a solid sphere (S) and a hollow sphere with thin walls (H), all having the same mass but…
• In the figure, the disc D does not slip on the surface S. The pulley P has mass, and the string does not slip on it…
• A light rigid rod of length L has a bob of mass M attached to one of its end just like a simple pendulum. Speed at the…
• Two particle of equal masses are revolving in circular paths of radii r 1 and r 2 respectively with the same speed. The…
• A cylindrical drum is pushed along by a board of length l . The drum rolls forward on the ground a distance of l/2…
• If the equation for the displacement of a particle moving on a circular path is given by : θ = 2t 3 + 0.5 where θ is in…
• A stone attached to one end of a string is revolved around a stick so that the string winds upon the stick and gets…
• A uniform rod of mass M = 2 kg and length L is suspended by two smooth hinges 1 and 2 as shown in the figure. A force F…
• A loop and a disc have the same mass and roll without slipping with the same linear velocity v. If the total K.E. of…
• A rod of length L is hinged from one end. It is brought to a horizontal position and released. The angular velocity of…
• If mass, speed and radius of rotation of a body moving in a circular path are all increased by 50%, the necessary force…
• In the given figure, a uniform solid sphere is released on the top of a fixed inclined plane of inclination 37° and…
• A solid cube of side 1 m is just tilted by a horizontal force of 10 N. The weight of cube is
• A constant external torque t acts for a very brief period Dt on a rotating system having moment of inertia I.
• A particle P will be in equilibrium inside a hemispherical bowl of radius 0.5 m at a height 0.2 m from the bottom when…
• Statement 1 : A rigid disc rolls without slipping on a fixed rough horizontal surface with uniform angular velocity…
• An inclined plane makes an angle of 30° with the horizontal. A solid sphere rolling down this inclined plane from rest…
• The maximum possible velocity of the bob at the lowest position of a simple pendulum of length L to oscillate is
• A uniform rod of mass m is bent into the form of a semicircle of radius R. The moment of inertia of the rod about an…
• A pair of uniform identical wires are bent into semi-circular rings, and then glued together so that the two rings have…
• A spherical ball rolls on a table without slipping. The fraction of its total energy associated with rotation is:
• A conical pendulum consists of a mass M suspended from a strong string of length l . The mass executes a circle of…
• A stone of mass m tied to a string of length l is rotating along a circular path with constant speed v. The torque on…
• A penguin of mass m falls from rest at point A. At horizontal distance d from the origin O (A) What is the angular…
• A particle is given an initial speed u inside a smooth spherical shell of radius R = 1 m that it is just able to…
• A solid sphere rolls down two different inclined planes of the same height but of different inclinations:
• Two particles A and B are moving as shown in figure. At this moment of time, the angular speed of A with respect to B…
• In the given figure, a uniform solid sphere is released on the top of a fixed inclined plane of inclination 37° and…
• Three identical rods, each of mass m and length l , form an equilateral triangle. Moment of inertia about one of the…
• A uniform bar of length 6a and mass 8m lies on a smooth horizontal table. Two-point masses m and 2m, moving in the same…
• A ball of mass m is attached to one end of a light rod of length l, the other end of which is hinged. What minimum…
• A hollow sphere is released from the top of an inclined plane of inclination q. Find the kinetic energy of the sphere…
• A smooth wire is bent into a vertical circle of radius a. A bead P can slide smoothly on the wire. the circle is…
• A disc of mass m and radius R moves in the x–y plane as shown the figure. The angular momentum of the disc about the…
• A particle is moving on a circular track of radius 30 cm with a constant speed of 6 m/s. It acceleration is :
• A stone of mass 1 kg tied to a light inextensible string of length 10/3 metre is whirled in a vertical circle. If the…
• A constant horizontal force F is applied on the top of a solid sphere and a hollow sphere of same mass and radius both…
• A body of mass 2 kg is tied at one end of a string 1 m long. The other end is fixed and the body revolves in a…
• Two racing cars of mass m 1 and m 2 are moving in circles of radii r 1 and r 2 respectively; their speeds are such that…
• A stick of length L and mass M lies on a frictionless horizontal surface on which it is free to move in any way. A ball…
• A sphere S rolls without slipping, moving with a constant speed on a plank P. The friction between the upper surface of…
• A particle of mass m is projected with a velocity v making an angle of 45° with the horizontal. The magnitude of the…
• A planet P revolves around the Sun in a circular orbit, with the sun at the centre, which is coplanar with and…
• A uniform sphere of mass m, radius r and moment of inertia I about its centre moves along the x-axis as shown in the…
• A particle of mass m is projected with a velocity v making an angle of 45° with the horizontal. The magnitude of the…
• A uniform beam of length L whose mass ‘m’ is 1.8 kg rests with its ends on two digital scales, as in figure. A uniform…
• Two particles A and B are situated at a distance d = 2m apart. Particle A has a velocity of 10 m/s at an angle of 60º…
• A wheel of radius r rolls without slipping with a speed v on a horizontal road. When it is at a point A on the road, a…
• From a circular disc of radius R and mass 9M , a small disc of radius R/3 is removed from the disc. The moment of…
• A thin uniform rod of mass m and length l is free to rotate about its upper end. When it is at rest, it receives an…
• Statement–1: Torque is equal to rate of change of angular momentum. Statement–2: Angular momentum depends on the moment…
• The kinetic energy of a particle moving along a circle of radius R depends on the distance covered s as T = Ks 2 where…
• A rod AB of length L revolves in a horizontal plane about the axis YY’ with an angular velocity . If A is area of…
• A circular turn table of radius 0.5 m has a smooth groove as shown in fig. A ball of mass 90 g is placed inside the…
• A wheel initially at rest, is rotated with a uniform angular acceleration. The wheel rotates through an angle q 1 in…
• A stone is rotated steadily in a horizontal circle with a time period T by means of a string of length l. If the…
• A particle moves in a circle of radius 25 cm at two revolutions per sec. The acceleration of the particle in m/s 2 is:
• A smooth table is placed horizontally and an ideal spring of spring constant k = 1000 N/m and unextended length of 0.5…
• Statement–1: The mass of a body cannot be considered to be concentrated at the centre of mass of the body for the…
• A mass of 2.9 kg, is suspended from a string of length 50 cm, and is at rest. Another body of mass 100 gm is moving…
• A thin rod of length 4 l and mass 4M is bent at the point as shown in the figure. What is the moment of inertia of the…
• Two rods 1 and 2 are released from rest as shown in figure. Given: l 1 = 4 l , m 1 = 2m, l 2 = 2 l and m 2 = m. There…
• A solid homogeneous sphere is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind…
• O is the centre of an equilateral triangle ABC. F 1 , F 2 and F 3 are three forces acting along the sides AB, BC and AC…
• A bob is suspended from a crane by a cable of length = 5 m. The crane and load are moving at a constant speed v 0 . The…
• The moment of inertia of a hollow cylinder of mass M, radius R and Length L about its axis is:
• When a mass is rotating in a plane about a fixed point its angular momentum is directed along
• A wheel of mass M and radius a and Moment of inertia IG (about centre of mass) is set rolling with angular velocity w…
• A fly wheel rotating about a fixed axis has a kinetic energy of 360 joule when its angular speed is 30 radian/sec. The…
• A simple pendulum is released from rest from the point A at an angle 30° with vertical. Then :
• A heavy small sized sphere is suspended by a string of length  . The sphere rotates uniformly in a horizontal circle…
• A metal rod of length L and mass m is pivoted at one end. A thin disk of mass M and radius R ( L ) is attached at its…
• Statement–I : Angular velocity is a characteristic of the rigid body as a whole. Statement-II : Angular velocity may be…
• A solid sphere of mass m is lying at rest on a rough horizontal surface. The coefficient of friction between the ground…
• A block of mass m, slides down along the surface of a bowl (radius R) from the rim to the bottom. The velocity of the…
• A uniform ladder of mass 10 kg leans against a smooth vertical wall making an angle of 53° with it. The other end rest…
• Let a_ r and a_ t represent radial and tangential acceleration. The motion of a particle may be circular if:
• A rigid spherical body is spinning around an axis without any external torque. Due to changes in temperature, the…
• A ring of 1 kg mass and 1 m radius is moving forward with velocity 1 m/s by rolling without slipping in a horizontal…
• A motorcyclist wants to drive on the vertical surface of wooden ‘well’ or radius 5 m, with a minimum speed of 5 5 m/s…
• A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its…
• A wheel of mass 2 kg, having practically all the mass concentrated along the circumference of a circle of radius 20 cm…
• The vertical section of a road over a canal bridge in the direction of its length is in the form of circle of radius…
• A mass m is hanged from a solid cylindrical shaft of radius R and mass 2m (as shown in the figure). Shaft is free to…
• The moment of inertia of a body about a given axis is 1.2 kg m 2 . Initially, the body is at rest. In order to produce…
• A circular disc rotates in a vertical plane about a fixed horizontal axis which passes through a point X on the…
• A streetlight of mass M is suspended from the end of a uniform rod of length L in different possible patterns as shown…
• Two rods 1 and 2 are released from rest as shown in figure. Given: l 1 = 4 l , m 1 = 2m, l 2 = 2 l and m 2 = m. There…
• A ball rolls down an inclined groove acquiring a velocity V_ T as it reaches the bottom. If the same ball slide without…
• In the given figure, a uniform solid sphere is released on the top of a fixed inclined plane of inclination 37° and…
• A particle moves in a uniform circular motion. Choose the wrong statement :
• For a particle of a rotating rigid body moving with constant angular velocity & v = rw So:
• A ring rolls without slipping on the ground. Its centre C moves with a constant speed u. P is any point on the ring…
• A disc of circumference s is at rest at a point A on a horizontal surface when a constant horizontal force begins to…
• Statement-I : The hard boiled egg and raw egg can be distinguished on the basis of spinning of both. Statement-II : The…
• Consider a wheel of a bicycle rolling on a level road at a linear speed V 0 . Choose the incorrect statement
• In the above question, the locus of the drops is a circle of radius :
• A car while travelling at a speed of 72 km/hr. Passes through a curved portion of road in the form of an arc of a…
• A car is moving with a speed of 30 m/sec on a circular path of radius 500 m. Its is increasing at the rate of 2 m/sec 2…
• A circular disc of Moment of inertia 0.5 kg m 2 and radius 0.2 m has a weightless string passing around its rim. The…
• An athlete diving off a high springboard can perform a variety of physical movements in the air before entering the…
• A particle performs uniform circular motion with an angular momentum L. If the frequency of particle’s motion is…
• A circular road of radius 1000 m has banking angle 45°. The maximum safe speed of a car having mass 200 kg will be, if…
• A small ball of mass m suspended from the ceiling at a point O by thread of length l moves along a horizontal circle…
• A uniform solid cylinder has a radius R and length L. If the moment of inertia of this cylinder about an axis passing…
• A hollow sphere is released from the top of an inclined plane of inclination q. What should be the minimum coefficient…
• A coin placed on a rotating turn table just slips if it is paced at a distace of 4 cm from the centre. If the angular…
• A cylindrical rod of mass M, length L and radius R has two cords wound around it whose ends are attached to the…
• The moment of inertia of a thin square plate ABCD, of uniform thickness about an axis passing through the centre O and…
• A body of mass m slides down an incline and reaches the bottom with a velocity u. If the same body were in the form of…
• The speed of a homogeneous solid sphere after rolling down an inclined plane of vertical height h from rest without…
• A solid sphere is rotating in free space. If radius of the sphere is increased keeping mass same which one of the…
• For a particle in uniform circular motion, the acceleration a at a point P ( R, ) on the circle of radius R is
• A solid sphere of radius R has moment of inertia I about its geometrical axis. it is melted into a disc of radius r and…
• If the banking angle of curved road is given by tan –1 (3/5) and the radius of curvature of the road is 6 m, then the…
• A horizontal bar of length l and negligible mass is supported at its two ends. A mass M is hung from the bar at a…
• Initial angular velocity of a circular disc of mass M is w 1 . Then two small spheres of mass m each are attached…
• A mass of 2 kg is whirled in a horizontal circle by means of a string at an initial speed of 5 rpm. Keeping the radius…
• A bicycle is performing pure rolling and moving at a speed of 30 km/h. Then speeds at the highest and lowest point of…
• A particle is moving along a circular path of radius 3 meter in such a way that the distance travelled measured along…
• A solid sphere and a hollow sphere of equal mass and radius are placed over a rough horizontal surface after rotating…
• A meter rule is freely pivoted about its centre. A piece of putty of mass 20 g travelling at 5 ms -1 strikes and…
• A round uniform body of radius R, mass M and moment of inertia I, rolls down (without slipping) an inclined plane…
• Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is…
• Statement–1: A disc is rolling on a rough horizontal surface. The instantaneous speed of the point of contact during…
• A particle of mass m is travelling with a constant velocity v = v _ 0 i along the line y = b, z = 0. Let dA be the area…
• The disc of radius r is confined to roll without slipping at A and B. If the plates have the velocities shown then:
• The moment of inertia of a system of four rods forming a square each of length L and mass M, about the axis shown is…
• A mass m is moving at speed v perpendicular to a rod of length d and mass M = 6 m which pivots around a frictionless…
• A circular disc of mass M 1 and radius R 1 initially moving with an angular speed w 0 about the horizontal centroidal…
• A simple pendulum 1 metre long has a bob of 10 kg. If the pendulum swings from a horizontal position, the K.E. of the…
• Statement–1: A sphere is performing pure rolling on a rough horizontal surface with constant angular velocity…
• A partcle rests on the top of a hemisphere of radiu R. Find the smallest horizontal velocity that must be imparted to…
• A uniform rod of length 2 l is placed with one end in contact with the horizontal table and is then inclined at an…
• A uniform rod of mass M = 2 kg and length L is suspended by two smooth hinges 1 and 2 as shown in the figure. A force F…
• A rod AB is 1 m long. It is hinged at A so as to rotate in a vertical plane. Initially the rod is horizontally placed…
• Two moving particles p and Q are 10 m apart at a certain instant. The velocity of P is 8 m/s making 30º with the line…
• A point moves along a circle with velocity v = at where a 0.5 m/sec 2 . Then the total acceleration of the point at the…
• A person slides freely down a frictionless inclined plane while his bag falls down vertically from the same height. The…
• A particle P is moving in a circle of radius ‘a’ with a uniform speed v. C is the centre of the circle and AP is…
• A racing car is travelling along a track at a constant speed of 40 m/s. A T.V. camera men is recording the event from a…
• A body is under the action of two equal and oppositely directed forces and the body is rotating with constant…
• Consider a uniform square plate of side a and mass m. The moment of inertia of this plate about an axis perpendicular…
• A particle of mass m is attached to one end of a string of length l while the other end is fixed to a point h above the…
• Statement–1: A solid sphere is rolling on a rough horizontal surface. Acceleration of contact point is zero…
• A pendulum of mass m is oscillating in a vertical circle with angular amplitude of 90°. The acceleration of the bob at…
• Statement 1: A uniform thin rod of length L is hinged about one of its end and is free to rotate about the hinge…
• A rigid horizontal smooth rod AB of mass 0.75 kg and length 40 cm can rotate freely about a fixed vertical axis through…
• A wet, open umbrella is held vertical and is twirled about the handle at a uniform rate of 21 revolutions in 44 second…
• A partcile of mass m is moving in a circular path of constant radius r such that its centripetal acceleration a c is…
• A gramophone record is revolving with an angular velocity ω . A coin is placed at a distance r from the centre of the…
• A car is moving with a speed v on a road inclined at an angle θ in a circular arc of radius r, the minimum coefficent…
• In the above problem, let t 1 and t 2 be the times when pure rolling of solid sphere and of hollow sphere is started…
• A string is wrapped several times round a solid cylinder and then the end of the string is held stationary while the…
• A rubber band of length l has a stone of mass m tied to its one end. It is whirled with speed v so that the stone…
• A motor car is travelling at 60 m/s on a circular road of radius 1200 m. It is increasing its speed at the rate of 4…
• A uniform rod of mass M = 2 kg and length L is suspended by two smooth hinges 1 and 2 as shown in the figure. A force F…
• An unbanked curve has a radius of 60 m. The maximum speed at which a car can make a turn if the coefficient of static…
• A hollow sphere and a solid sphere of same mass and radius are allowed to roll down an inclined plane from same height…
• Four identical rods, each of mass m and length l , are joined to form a rigid square frame. The frame lies in the x-y…
• A uniform ball of radius r rolls without slipping down from the top of a sphere of radius R. The angular velocity of…
• A mass M is moving with constant velocity parallel to x–axis. Its angular momentum with respect to origin.
• A rod AC of length l and mass m is kept on a horizontal smooth plane. It is free to rotate and move. A particle of same…
• A disc of radius R and mass M is rolling horizontally without slipping with speed v. It then moves up an incline as…
• Two thin discs, each of mass M and radius r, are attached as shown in the figure, to form a rigid body. The rotational…
• Two rods 1 and 2 are released from rest as shown in figure. Given: l 1 = 4 l , m 1 = 2m, l 2 = 2 l and m 2 = m. There…
• A ring, hollow sphere and solid sphere are rolled down from inclined plane. Which will take least time to reach the…
• In the following figure a massive rod AB of length is held in horizontal position by two massless strings. If the…
• A ring of radius r and mass m rotates about an axis passing through its centre and perpendicular to its plane with…
• A uniform disc of radius a and mass m is rotating freely with angular speed in a horizontal plane, about a smooth fixed…
• A mass M is supported by a massless string wound around a uniform cylinder of mass M and radius R. On releasing the…
• In the above question, the tangential speed of the water drop on leaving the rim of the umbrella is :
• A toy car travels in horizontal circle of radius 2a, kept on the track by a radial elastic string. Its period is T. The…
• A circular disc is to be made using iron and aluminium. To keep its moment of inertia maximum about a geometrical axis…

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