If the volume of the Earth suddenly shrinks to $1/64$ of its present volume without any change in its mass,then the duration of the day on Earth will be ..... hours.

$A$ uniform disc of mass $M$ is rotating with a constant angular velocity $\omega$ about an axis passing through its center and perpendicular to its plane. Let its angular momentum be $L$. $A$ drop of molten plastic falls onto the disc and sticks to it. Which of the following remains constant?

$A$ person standing on a rotating table holds weights in their outstretched hands and is rotating. They suddenly pull their hands in close to their body. Which statement is true?

Given below are two statements: One is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A)$ : In a conical pendulum,angular momentum about its vertical axis remains constant.
Reason $(R)$ : Net torque about the vertical axis of a conical pendulum is not zero.
In the light of the above statements,choose the most appropriate answer from the options given below:

$A$ ring of mass $M$ and radius $R$ is rotating about its axis with angular velocity $\omega$. Two identical bodies each of mass $m$ are now gently attached at the two ends of a diameter of the ring. Because of this,the kinetic energy loss will be

$A$ child with mass $m$ is standing at the edge of a disc with moment of inertia $I$,radius $R$,and initial angular velocity $\omega$. See the figure given below. The child jumps off the edge of the disc with tangential velocity $v$ with respect to the ground. The new angular velocity of the disc is