The variation of angular acceleration $\alpha$ of a point on a rigid body rotating about a fixed axis with time $t$ is shown in the figure. What is the sense of rotation of the rod? (Assume clockwise as negative)

$A$ solid disc has a diameter of $0.5 \ m$ and a mass of $16 \ kg$. What torque must be applied to increase its angular velocity from $0$ to $120 \ rpm$ in $8 \ s$?

$A$ thin uniform rod is pivoted at $O$. It rotates in a horizontal plane with a constant angular velocity $\omega$. At $t = 0$,a small insect starts moving from $O$ towards the other end with a constant speed $v$ relative to the rod. It reaches the other end at $t = T$ and stops. The angular velocity $\omega$ of the system remains constant. Which of the following graphs best represents the magnitude of the torque $|\tau|$ at $O$ as a function of time $t$?

$A$ rod $PQ$ of mass $M$ and length $L$ is hinged at end $P$. The rod is kept horizontal by a massless string tied to point $Q$ as shown in the figure. When the string is cut,the initial angular acceleration of the rod is

In the given figure,about which axis will the angular acceleration be greater if a force is applied at the midpoint of the triangular frame?

$A$ 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 $\,N$)