$A$ rod of mass $M$ and length $L$ is placed in a horizontal plane. One of its ends is hinged on a vertical axis. $A$ horizontal force $F = Mg/2$ is applied at a distance of $5L/6$ from the hinged end. What will be the angular acceleration of the rod?

$A$ circular disc of radius $2 \ m$ is rotating at $240 \ rpm$. If a torque is applied to the disc, it slows down at a rate of $\pi \ rad/s^2$. How long will it take to stop? How many revolutions will the disc complete before coming to rest?

Moment of inertia of a body about a given axis is $1.5\, kg\, m^2$. Initially,the body is at rest. In order to produce a rotational kinetic energy of $1200\, J$,an angular acceleration of $20\, rad/s^2$ must be applied about the axis of rotation for a duration of ......... $\sec$.

$A$ flywheel is rotating at a rate of $150 \text{ rev/minute}$. If it slows at a constant retardation of $\pi \text{ rad/s}^2$, then the time required for the wheel to come to rest is (in $\text{ s}$)

$A$ thin solid disk of $1 \ kg$ is rotating along its diameter axis at the speed of $1800 \ rpm$. By applying an external torque of $25 \pi \ Nm$ for $40 \ s$,the speed increases to $2100 \ rpm$. The diameter of the disk is . . . . . . $m$.

$A$ wheel of radius $0.2 \ m$ rotates freely about its center when a string that is wrapped over its rim is pulled by a force of $10 \ N$ as shown in the figure. The established torque produces an angular acceleration of $2 \ rad/s^2$. The moment of inertia of the wheel is . . . . . . $kg \ m^2$. (Acceleration due to gravity $= 10 \ m/s^2$)