An automobile moves on a road with a speed of $54km{h}^{\mathit{-}\mathit{1}}$ The moment of inertia about its axis of rotation is $3kg{m}^{\mathit{2}}$. If the vehicle is brought to rest in $15s$, the magnitude of average torque transmitted by its brakes to the wheel is

Point masses $m_{1 }$and $m_2$ are placed at the opposite ends of a rigid rod of length $L$, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point $P$ on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity ${\text{ω}}_0$ is minimum, is given by:-
   

What will be the value of the maximum acceleration of the truck in the forward direction so that the block kept on, the back does not topple?

A solid cylinder of radius $5 \mathrm{cm}$ is pure rolling on $30°$ inclined plane. Find out angular velocity after it travels $6 \mathrm{m}$ on an incline plane.