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) 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.

Calculate the moment of inertia of a ring about in axis passing through centre and perpendicular to its plane.

Find an expression for MI of a thin circular RING about an axis passing through its centre and perpendicular to the plane of the ring.

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?

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 parabola has it vertex at the origin, axis along the X-axis and it passes through the point (4, -8). Find its equation.

Find the equation of the straight line passing through the point (i) (-1, 2) and parallel to 3x - 4y + 1 =0

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?