Why is it easier to rotate a disc than a ring of the same mass and size, about an axis passing through their centres?

Why does a solid sphere have smaller moment of inertia than a hollow cylinder of same mass and radius, about an axis passing through their axes of symmetry?

A conducting rod of 1 m length is rotated with a frequency of 50 rev/s, with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius 1 m, about an axis passing through the centre and perpendicular to the plane of the ring. A constant and uniform magnetic field of 1 T parallel to the axis is present everywhere. What is the emf between the centre and the metallic ring?

What is torque due to gravity about an axis passing through C.M.?

Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. Hie cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time.

A steel rod of length 2l, cross sectional area A and mass M is set rotating in a horizontal plane about an axis passing through the centre. If Y is the Young's modulus for steel, find the extension in the length of the rod. (assume the rod is uniform).

Two spheres each of mass M and radius R//2 are connected with a massless rod of lenth 2R as shown in fig.What will be the oment of inertia of the system about an axis passing through the centre of one of the spheres and prependicular to the rod?

Consider a light beam incident from air to a glass slab at Brewster's angle as shown in Fig. EP 10.1. A polarised is placed in the path of the emergent ray at point P and rotated about an axis passing through the center and perpendicular to the plane of the polaroid.

Three thin metal rods,each of mas M and length dL,are welded to form an equilateral triangle.The moment of inertia of the composite structure about an axis passing through the centre of mas of the structure and perpendicualr to its plane is :