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

$A$ door $1.6 \,m$ wide requires a force of $1 \,N$ to be applied at the free end to open or close it. The force that is required at a point $0.4 \,m$ distance from the hinges for opening or closing the door is (in $\,N$)

How many degrees of freedom does a rigid body have for a rotational motion about a fixed axis?

$A$ body rotates about a stationary axis. If the angular deceleration is proportional to the square root of the angular speed, then the mean angular speed of the body, given $\omega_0$ as the initial angular speed, is

Two small balls are fixed at the ends of a light rigid rod of length $L = 0.4 \ m$. The system is released from a height $h = 5 \ m$ with the rod horizontal. The balls collide with the horizontal surface and rebound. The coefficient of restitution between ball $A$ and the ground is $e_A = 0.6$ and that between ball $B$ and the ground is $e_B = 0.4$. Find the angular speed (in $rad/s$) of the rod just after the collision. Take the acceleration due to gravity $g = 10 \ m/s^2$.

$A$ plank with a uniform sphere placed on it rests on a smooth horizontal plane. The plank is pulled to the right by a constant force $F$. If the sphere does not slip over the plank,which of the following is true?