If the earth were to suddenly contract to $\frac{1}{n}^{th}$ of its present radius without any change in its mass,the duration of the new day will be nearly:

$A$ circular platform is free to rotate in a horizontal plane about a vertical axis passing through its center. $A$ tortoise is sitting at the edge of the platform. Now, the platform is given an angular velocity $\omega_0$. When the tortoise moves along a chord of the platform with a constant velocity (with respect to the platform), the angular velocity of the platform $\omega(t)$ will vary with time $t$ as:

The angular momentum of a particle performing circular motion under a central force is constant because of .........

$A$ particle of mass $m$ moves with a velocity $v_0$ in a circle of radius $R_0$ on a smooth horizontal plane. The mass is tied to a string passing through a hole in the smooth plane as shown in the figure. The tension in the string is gradually increased,and finally,the mass $m$ moves in a circle of radius $\frac{R_0}{2}$. What is the ratio of the final kinetic energy to the initial kinetic energy?

What is combined translation and rotation motion?

$A$ disc of mass $M$ and radius $R$ is rolling with angular speed $\omega$ on a horizontal plane as shown. The magnitude of angular momentum of the disc about the origin $O$ is