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

$A$ uniform metre stick of mass $M$ and length $L = 1 \ m$ is hinged at one end and supported in a horizontal direction by a string attached to the other end. What should be the initial angular acceleration of the free end of the stick if the string is cut? (in $rad/s^2$)

$A$ hollow sphere of mass $1 \,kg$ and radius $10 \,cm$ is free to rotate about its diameter. If a force of $30 \,N$ is applied tangentially to it,its angular acceleration is (in $rad/s^2$):

$A$ flywheel of moment of inertia $0.4 \, kg \, m^2$ and radius $0.2 \, m$ is free to rotate about a central axis. If a string is wrapped around it and it is pulled with a force of $10 \, N$,then the angular velocity after $4 \, s$ will be ......... $rad \, s^{-1}$.

$A$ 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 ...... $N$.

$A$ solid sphere of mass $2 \,kg$ and radius $1 \,m$ is free to rotate about an axis passing through its centre. $A$ constant tangential force $F$ is required to rotate the sphere with $10 \,rad/s$ in $2 \,s$ starting from rest. The value of $F$ is . . . . . . (in $\,N$)