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 ratio of the radii of two solid spheres of same mass is $2: 3$. The ratio of the moments of inertia of the spheres about their diameter is

A particle of mass $m$ is moving along a line $y=x+a$ with a constant velocity $v$. The angular momentum of the particle about the origin is