A constant torque acting on a uniform circular wheel changes its angular momentum from $A_0$ to $4 A_0$ in 4 seconds. The magnitude of the torque is

A particle performs uniform circular motion with an angular momentum $L$. If the frequency of the particle's motion is doubled and its kinetic energy is halved, then its angular momentum becomes

The displacement of a particle is given by the relation $x=4(\cos \pi t+\sin \pi t)$. The amplitude of the particle is

A body of mass $m$ is at height $R$ from the surface of the earth where $R$ is the radius of the earth. If the body is taken from here to a height of $3 R$ from the surface of the earth, the increase in the gravitational potential energy of the body is

( $g$ is acceleration due to gravity on the surface of the earth)