An air compressor is powered by a $200\,rad\,s^{-1}$ electric motor using a $V-$ belt drive. The motor pulley is $8\,cm$ in radius, and the tension in the $V-$ belt is $135\,N$ on one side and $45\,N$ on the other. The power of the motor will be …… $kW$.

A rod of length $l$ is hinged from one end. It is brought to a horizontal position and released. The angular velocity of the rod when it is in the vertical position is

A uniform ring of radius $R$ is moving on a horizontal surface with speed $v$, then climbs up a ramp of inclination $30^{\circ}$ to a height $h$. There is no slipping in the entire motion. Then, $h$ is

A thin rod of mass $m$ and length $l$ is oscillating about horizontal axis through its one  end. Its maximum angular speed is $\omega$. Its centre of mass will rise upto maximum  height :-

A cord is wound round the circumference of wheel of radius $r$. The axis of the wheel is horizontal and moment of inertia about it is $I$. A weight $mg$ is attached to the end of the cord and falls from rest. After falling through a distance $h$, the angular velocity of the wheel will be