$A$ body rotates about a fixed axis with an angular acceleration of $3 \, rad/s^2$. The angle rotated by it during the time when its angular velocity increases from $10 \, rad/s$ to $20 \, rad/s$ (in radian) is ..........

$A$ solid cylinder of mass $50\, kg$ and radius $0.5\, m$ is free to rotate about a horizontal axis. $A$ massless string is wound around the cylinder with one end attached to it and the other hanging freely. The tension in the string required to produce an angular acceleration of $2\, \text{revolutions } s^{-2}$ is ...... $N$.

The grinding stone of a flour mill is rotating at $600 \, rad/s$. For this, a power of $1.2 \, kW$ is used. The effective torque on the stone in $N-m$ will be:

In the figure $(a)$,half of the meter scale is made of wood while the other half is made of steel. The wooden part is pivoted at $O$. $A$ force $F$ is applied at the end of the steel part. In figure $(b)$,the steel part is pivoted at $O'$ and the same force $F$ is applied at the wooden end (in a horizontal plane). Which of the following is true?

$A$ wheel with a moment of inertia of $5 \times 10^{-3} \ kg \cdot m^2$ is rotating at a rate of $20 \ rev/s$. The torque required to bring it to rest in $10 \ s$ is:

$A$ light rope is wound around a hollow cylinder of mass $5\,kg$ and radius $70\,cm$. The rope is pulled with a force of $52.5\,N$. The angular acceleration of the cylinder will be.....$rad\,s^{-2}$.