$A$ boy is standing at the center of a turntable holding two blocks in his hands. The rotational kinetic energy of the system about the axis passing through the center is $K$. When the boy extends his arms,the moment of inertia of the system about the axis of rotation doubles. What will be the new rotational kinetic energy of the system?

If the radius of the earth is reduced to three-fourth of its present value without any change in its mass,then the duration of the day on earth will be . . . . . . hours $30$ minutes.

$A$ bullet of mass $10 \; g$ and speed $500 \; m/s$ is fired into a door and gets embedded exactly at the centre of the door. The door is $1.0 \; m$ wide and weighs $12 \; kg$. It is hinged at one end and rotates about a vertical axis practically without friction. Find the angular speed of the door just after the bullet embeds into it.

$A$ horizontal disc of moment of inertia $4.25 \,kg \cdot m^2$ with respect to its axis of symmetry is spinning counter-clockwise at $15 \,rps$ about its axis,as viewed from above. $A$ second disc of moment of inertia $1.80 \,kg \cdot m^2$ with respect to its axis of symmetry is spinning clockwise at $25 \,rps$ as viewed from above about the same axis and is dropped on top of the first disc. The two discs stick together and rotate as one about their axis of symmetry. The new angular velocity of the system as viewed from above is close to

$A$ thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Two objects,each of mass $m$,are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity:

$A$ child is standing at the center of a rotating platform with hands folded. The kinetic energy of the system is $K$. The child now stretches his hands,doubling the moment of inertia. The kinetic energy of the system will now become ........