Exercise (Conceptual Questions)

Essential characteristic of equilibrium is

Two particles having masses $\mathrm{M}$ and $m$are moving in a circular path having radius $\mathrm{R}$ and $r .$ If their time periods are same, then ratio of angular velocity will be

The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of same radius about a tangential axis in the plane of the ring is

A particle of mass $M$ and radius of gyration $K$ is rotating with angular acceleration $\alpha$. The torque acting on the particle is,

A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is $K.$ If radius of the ball be $R,$ then the fraction of total energy associated with its rotational energy will be

The ratio of time taken by a uniform solid sphere and disc of the same mass and the same diameter to roll down through the same distance from rest on a smooth inclined plane is:

When a sphere of the moment of inertia $I$ rolls down on an inclined plane the percentage of total energy which is, rotational, is approximate: 

When a body starts to roll on an inclined plane, its potential energy is converted into: