The angular momentum of a particle performing uniform circular motion is $L$. If the kinetic energy of the particle is doubled and the frequency is halved,then the new angular momentum becomes:

$A$ uniform rod of mass $M$ is hinged at its upper end. $A$ particle of mass $m$ moving horizontally strikes the rod at its mid-point elastically. If the particle comes to rest after the collision,find the value of $M/m$.

Two rings of the same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the rings is (mass of the ring $= m$,radius $= r$)

$A$ ring rolls without slipping on the ground. Its centre $C$ moves with a constant speed $u$. $P$ is any point on the ring. The speed of $P$ with respect to the ground is:

The graphs below show angular velocity $\omega$ as a function of time $t$. In which one is the magnitude of the angular acceleration $\alpha$ constantly decreasing?

$A$ bullet of mass $m$ is fired horizontally into a large sphere of mass $M$ and radius $R$ resting on a smooth horizontal table. The bullet hits the sphere at a height $h$ from the table and sticks to its surface. If the sphere starts rolling without slipping immediately on impact,then