If the Earth shrinks to $1/8$ of its original volume, while maintaining the same mass, then the duration of the day will be (in $hrs$)

$A$ rigid spherical body is spinning around an axis without any external torque. Due to a change in temperature,the volume increases by $1\%$. Its angular speed:

$A$ thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect,the angular speed of the disc

$A$ force $\overrightarrow{F} = \alpha \hat{i} + 3\hat{j} + 6\hat{k}$ is acting at a point $\overrightarrow{R} = 2\hat{i} - 6\hat{j} - 12\hat{k}$. The value of $\alpha$ for which angular momentum about the origin is conserved is

$A$ circular disk of moment of inertia $I_t$ is rotating in a horizontal plane,about its symmetry axis,with a constant angular speed $\omega_i$. Another disk of moment of inertia $I_b$ is dropped coaxially onto the rotating disk. Initially,the second disk has zero angular speed. Eventually,both the disks rotate with a constant angular speed $\omega_f$. The energy lost by the initially rotating disk to friction is

$A$ dancer on a smooth floor is spinning about a vertical axis at an angular velocity of $20 \ rad/s$ with her arms folded. When she stretches her arms out,the angular speed decreases to $10 \ rad/s$. If the initial moment of inertia of the dancer is $I$,what will be the new moment of inertia?