$A$ particle of mass $m$ moves in a circular path of radius $r$,under the action of a force which delivers constant power $P$ and increases its speed. The angular acceleration of the particle at time $t$ is proportional to:

$A$ wheel has a moment of inertia $5 \times 10^{-3} \, kg \, m^2$ and is making $20 \, rev/sec$. The torque needed to stop it in $10 \, sec$ is $............. \times 10^{-2} \, N-m$. (in $\pi$)

$A$ horizontal heavy uniform bar of weight $W$ is supported at its ends by two men. At the instant one of the men lets go of his end of the rod,the force on the other man's hand changes to:

$A$ same torque is applied to a disc and a ring of equal mass and radii. Then:

$A$ 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 $= 10 \ m/s^2$)

The engine of a motor vehicle develops a power of $100 \, kW$. If it rotates at a speed of $1800 \, rpm$,the torque exerted by it is ...... $N-m$.