A small mass attached to a string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will

The instantaneous angular position of a point on a rotating wheel is given by the equation $$\theta \left( t \right) = 2{t^3} - 6{t^2}$$

The torque on the wheel becomes zero at

The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is $$I$$₀. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

From a circular disc of radius R and mass 9M, a small disc of mass M and radius $${R \over 3}$$ is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is