$A$ uniform rod of mass $m$ and length $l$ is suspended by means of two identical inextensible light strings as shown in the figure. The tension in one string immediately after the other string is cut is . . . . . . . ($g$ is the acceleration due to gravity)

The spool shown in the figure is placed on a rough horizontal surface and has an inner radius $r$ and an outer radius $R$. The angle $\theta$ between the applied force and the horizontal can be varied. The critical angle $\theta$ for which the spool does not roll and remains stationary is given by:

$A$ massless string is wrapped around a disc of mass $M$ and radius $R$. Another end is tied to a mass $m$ which is initially at height $h$ from the ground level as shown in the figure. If the mass is released,then its velocity while touching the ground level will be:

$A$ body is in pure rotation. The linear speed $v$ of a particle,the distance $r$ of the particle from the axis,and the angular velocity $\omega$ of the body are related as $\omega = \frac{v}{r}$. Thus,

$A$ rigid body is rotating with variable angular velocity $\omega = (a - bt)$ at any instant of time $t$. The total angle subtended by it before coming to rest will be ($a$ and $b$ are constants).

The plank in the figure moves a distance $100 \ mm$ to the right while the centre of mass of the sphere of radius $150 \ mm$ moves a distance $75 \ mm$ to the left. The angular displacement of the sphere (in radian) is (there is no slipping anywhere):-