The moment of inertia of a solid cylinder of mass 2.5 kg and radius 10 cm about its axis is

A circular dise of diameter 0.8 m and mass 4 kg is rolling on a smooth horizontal plane. If 2.56 N m torque is acting on the disc, then its angular acceleration is

A solid sphere and a solid cylinder have same mass and same radius. The ratio of the moment of inertia of the solid sphere about its diameter and the moment of inertia of the solid cylinder about its axis is

If a solid sphere is rolling without slipping on a horizontal plane, then the ratio of its rotational and total kinetic energies is

As shown in the figure, two thin coplanar circular discs $A$ and $B$ each of mass $M^{\prime}$ and radius ' $r$ ' are attached to form a rigid body. The moment of inertia of this system about an axis perpendicular to the plane of disc $B$ and passing through its centre is

A circular disc of mass 20 kg and radius 1 m is rotating about an axis passing through its centre and perpendicular to its plane with an angular velocity of $2 \mathrm{rad} \mathrm{s}^{-1}$. Then, the rotational kinetic energy of the disc is

Radius of gyration of a thin uniform rod of length ' $L$ ' about an axis passing through its centre and perpendicular to its length is

A thin circular ring and a circular disc of equal mass are rolling without sliding. If their linear velocities are equal and the total kinetic energy of the disc is 6 J , then the total kinetic energy of the ring is

A solid sphere of mass 4 kg and radius 28 cm is on an inclined plane. If the acceleration of the sphere when it rolls down without sliding is $3.5 \mathrm{~ms}^{-2}$, then the acceleration of the sphere when it slides down without rolling is

A thin uniform circular disc rolls with a constant velocity without slipping on a horizontal surface. Its total kinetic energy is

Three thin uniform rods each of mass $M$ and length $L$ are placed along the three axes of a cartesian co-ordinate system with one end of all the rods at origin. The moment of inertia of the system of the rods about $Z$-axis is

If the radius of gyration of a thin circular ring about an axis passing through its centre and perpendicular to its plane is $10 \sqrt{2} \mathrm{~cm}$, then its radius of gyration about its diameter is

If a wheel starting from rest is rotating with an angular acceleration of $\pi \mathrm{rad} \mathrm{s}^{-2}$, then the number of rotations made by the wheel in the first 6 seconds time is

The moment of inetia of a rod about an axis passing through its centre and perpendicular to its length is $\frac{1}{12} M L^2$, where $M$ is the mass and $L$ is the length of the rod. The rod is bent in the middle, so that the two halves make an angle of $60^{\circ}$. The moment of inertia of the bent rod about the same axis would be

A solid cylinder of radius $$R$$ is at rest at a height $$h$$ on an inclined plane. If it rolls down then its velocity on reaching the ground is

A solid sphere of radius $$R$$ has its outer half removed, so that its radius becomes $$(R / 2)$$. Then its moment of inertia about the diameter is

Consider a disc of radius $$R$$ and mass $$M$$. A hole of radius $$\frac{R}{3}$$ is created in the disc, such that the centre of the hole is $$\frac{R}{3}$$ away from centre of the disc. The moment of inertia of the system along the axis perpendicular to the disc passing through the centre of the disc is

As solid sphere of mass $$M$$ and radius $$R$$ spins about an axis passing through its centre making $$600 \mathrm{~rpm}$$. Its kinetic energy of rotation is

Two fly wheels $$A$$ and $$B$$ are mounted side by side with frictionless bearings on a common shaft. Their moments of inertia about the shaft are $$5.0 \mathrm{~kg}-\mathrm{m}^2$$ and $$20.0 \mathrm{~kg}-\mathrm{m}^2$$, respectively. Wheel $$A$$ is made to rotate at $$10 \mathrm{~rev}$$ per second. Wheel $$B$$, initially stationary, is now coupled to $$A$$ with the help of a clutch. The rotation speed of the wheels will become

A sphere and a hollow cylinder withoutslipping, roll down two separate inclinedplanes A and B, respectively. They cover samedistance in a given duration. If the angle ofinclination of plane A is 30$$^\circ$$, then the angleof inclination of plane B must be(approximately)

Four spheres each of diameter $$2 a$$ and mass $$m$$ are placed in a way that their centers lie on the four corners of a square of side $$b$$. Moment of inertia of the system about an axis along one of the sides of the square is

If an energy of 684 J is needed to increase thespeed of a flywheel from 180 rpm to360 rpm, then find its moment of inertia.

A sphere of mass m is attached to a spring ofspring constant k and is held in unstretchedposition over an inclined plane as shown inthe figure. After letting the sphere go, findthe maximum length by which the springextends, given the sphere only rolls.

A girl of mass M stands on the rim of africtionless merry-go-round of radius R androtational inertia I, that is not moving. Shethrows a rock of mass m horizontally in adirection that is tangent to the outer edge ofthe merry-go-round. The speed of the rock,relative to the ground is v. Afterwards, thelinear speed of the girl is

Which of the following type of wheels ofsame mass and radius will have largestmoment of inertia?