If the radius of the Earth becomes $1/n^{th}$ of its present value,without any change in its mass,then the duration of the day becomes:

$A$ small object is attached to a light string which passes through a hollow tube. The tube is held by one hand and the string by the other. The object is set into rotation in a circle of radius $r_1$. The string is then pulled down,shortening the radius of the circle to $r_2$. The ratio of the new kinetic energy to the original kinetic energy is

When a body is spinning on its axis in the absence of any external torque,choose the wrong statement.

$A$ swimmer curls their body before entering the water so that...

$A$ circular platform is mounted on a frictionless vertical axle. Its radius $R = 2\, m$ and its moment of inertia about the axle is $200\, kg\, m^2$. It is initially at rest. $A$ $50\, kg$ man stands on the edge of the platform and begins to walk along the edge at the speed of $1\, m/s$ relative to the ground. Time taken by the man to complete one revolution is

$A$ uniform circular disc of mass $50 \ kg$ and radius $0.4 \ m$ is rotating with an angular velocity of $10 \ rad \ s^{-1}$ about its own axis,which is vertical. Two uniform circular rings,each of mass $6.25 \ kg$ and radius $0.2 \ m$,are gently placed symmetrically on the disc in such a manner that they are touching each other along the axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest relative to the disc and the system rotates about the original axis. The new angular velocity (in $rad \ s^{-1}$) of the system is: