Moment of Inertia & Radius of Gyration: JEE Questions & Solutions

Two identical thin rods of mass M kg and length L m are connected as shown in figure. Moment of inertia of the combined rod system about an…

The pulley shown in figure is made using a thin rim and two rods of length equal to diameter of the rim. The rim and each rod have a mass…

A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm. The moment of…

A circular disc has radius R1 and thickness T1. Another circular disc made of the same material has radius R2 and thickness T2. If the…

A uniform bar of length 12 cm and mass 20m lies on a smooth horizontal table. Two point masses m and 2m are moving in opposite directions…

The moment of inertia of a square loop made of four uniform solid cylinders, each having radius R and length L (R L) about an axis passing…

Two small balls with masses m and 2m are attached to both ends of a rigid rod of length d and negligible mass. If angular momentum of this…

Suppose there is a uniform circular disc of mass M kg and radius r m shown in figure. The shaded regions are cut out from the disc. The…

Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm. When released from…

A uniform solid cylinder of length L and radius R has moment of inertia about its axis equal to I1. A small co-centric cylinder of length…

A solid sphere of radius 10 cm is rotating about an axis which is at a distance 15 cm from its centre. The radius of gyration about this…

A uniform circular disc of radius R and mass M is rotating about an axis perpendicular to its plane and passing through its center. A small…

The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in a…

Two iron solid discs of negligible thickness have radii R1 and R2 and moment of inertia I1 and I2, respectively. For R2 = 2R1, the ratio of…

A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of the wheel is 10 kg and…

Moment of inertia of a rod of mass M and length L about an axis passing through its center and normal to its length is. Now the rod is cut…

A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by a force of 10 N as shown in…

A solid sphere with uniform density and radius R is rotating initially with constant angular velocity ( 1) about its diameter. After some…

A, B and C are disc, solid sphere and spherical shell respectively with the same radii and masses. These masses are placed as shown in the…

M and R be the mass and radius of a disc. A small disc of radius R3 is removed from the bigger disc as shown in figure. The moment of…

A rod of linear mass density and length L is bent to form a ring of radius R. Moment of inertia of the ring about any of its diameter is:

A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm. By applying an external torque of 25 Nm for 40 s,…

A solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm, then its radius of gyration about PQ will be x cm. The…

A uniform solid cylinder with radius R and length L has moment of inertia I1, about the axis of the cylinder. A concentric solid cylinder…

A thin uniform rod of length 2 m, cross-sectional area ‘A’ and density ‘d’ is rotated about an axis passing through the center and…

Two discs of the same mass and different radii are made of different materials such that their thicknesses are 1 cm and 0.5 cm…

A ring and a solid sphere rotating about an axis passing through their centers have the same radii of gyration. The axis of rotation is…

The moment of inertia of a semicircular ring about an axis, passing through the center and perpendicular to the plane of the ring, is…

If the Earth suddenly shrinks to 164th of its original volume with its mass remaining the same, the period of rotation of the Earth becomes…

A circular plate is rotating horizontal plane, about an axis passing through its center perpendicular to the plate, with an angular…

A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is pulled with a force of 52.5 N. The angular…

A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radii…