$A$ uniform disc is rolling on a horizontal surface. At a certain instant $B$ is the point of contact and $A$ is at height $2R$ from ground, where $R$ is radius of disc.

$A$ time varying force $F = 2t$ is applied on a spool rolling as shown in figure. The angular momentum of the spool at time $t$ about bottommost point is:

A particle is moving along a straight line parallel to $x-$ axis with constant velocity. Its angular momentum about the origin

A solid cylinder of mass $2\ kg$ and radius $0.2\,m$ is rotating about its own axis without friction with angular velocity $3\,rad/s$. A particle of mass $0.5\ kg$ and moving with a velocity $5\ m/s$ strikes the cylinder and sticks to it as shown in figure. The angular momentum of the cylinder before collision will be …….. $J-s$

Two rigid bodies $A$ and $B$ rotate with rotational kinetic energies $E_A$ and $E_B$ respectively.  The moments of inertia of $A$ and $B$ about the axis of rotation are $I_A$ and $I_B$ respectively. If $I_A = I_B/4 \,$and$ \, E_A = 100\ E_B$ the ratio of angular momentum $(L_A)$ of $A$ to the angular momentum $(L_B)$ of $B$ is