$A$ disc rolls on a horizontal surface (without slipping). $C$ is the center and $Q$ and $P$ are two points at the same distance from $C$. Let $v_P$,$v_Q$,and $v_C$ be the magnitudes of the velocities of points $P$,$Q$,and $C$ respectively. Then:

$A$ rod of length $l$ is held vertically stationary with its lower end located at a point $P$ on a horizontal plane. When the rod is released to topple about $P$, the velocity of the upper end of the rod with which it hits the ground is

There is a rod of length $l$. The velocities of its two ends are $v_1$ and $v_2$ in opposite directions normal to the rod. The distance of the instantaneous axis of rotation from $v_1$ is:

$A$ cubical block of side $L$ rests on a rough horizontal surface with coefficient of friction $\mu$. $A$ horizontal force $F$ is applied on the block as shown. If the coefficient of friction is sufficiently high so that the block does not slide before toppling,the minimum force required to topple the block is

$A$ thin rod $AB$ is sliding between two fixed right-angled surfaces. At some instant,its angular velocity is $\omega$. If $I_X$ represents the moment of inertia of the rod about an axis perpendicular to the plane and passing through the point $X$ ($A, B, C,$ or $D$),the kinetic energy of the rod is:

$A$ disc is rolling (without slipping) on a horizontal surface. $C$ is its center and $Q$ and $P$ are two points on the disc such that $Q$ is further from the contact point $O$ than $C$,and $P$ is closer to the contact point $O$ than $C$. Let $V_P, V_Q$ and $V_C$ be the magnitudes of the velocities of points $P, Q$ and $C$ respectively,then: