Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The 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?

Two solid sphere of the same mass and same radius, one solid and other hollow. Which one have greater moment of inertia about a diameter?

A ring and a circular disc of different materials have equal masses and equal radii. Which one will have a larger moment of inertia about an axis passing through its centre of mass perpendicular to its plane?

Given the M.I. of a dise of mass M and radius R about any of its diameter to be MR^2 /4. Find its M.I about an axis (i) passing through its centre and normal to it, and (ii) passing through a point at its edge and normal to it.

A thin dielectric disc uniformly distritbuted with charge q has radius r and is rotated n times per second about an axis perpendicular to the disc and passing through the centre. Find the magnetic induction at the centre of the disc.

Define moment of inertia and radius of gyration. Deduce an expression for MI of a circular disc about an axis passing through its centre. Two circular discs have their masses in the ratio 1:2 and their diameters 2:1 . Calculate the ratio of their moments of inertia

A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s-^1. The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be 2MR^2IS, where M is the mass of the sphere and R is the radius of the sphere(b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be MR2I4, find its moment of inertia about an axis normal to the' disc and passing through a point on its edge.

MI of a thin circular disc about an axis passing through its centre and perpendicular to its plane is 1/2 MR^2 , where M is the mass of the disc and R is its radius. Find an expression for radius of gyratiuon of the disc about an axis tangential to the edge and peerpendicular to the plane of rotation.