A particle performs uniform circular motion with an angular momentum $L.$ If the frequency of the particle motion is doubled keeping the radius constant, the angular momentum becomes

A disc of mass $m_0$ rotates freely about a fixed horizontal axis through its centre. A thin cotton pad is fixed to its rim, which can absorb water?

The mass of water dripping onto the pad is $\mu$ per second. After what time will the angular velocity of the disc get reduced to half of its initial value?

A uniform rod $AB$ of length $7 \mathrm{m}$ is undergoing combined rotational and translational motions such that at some instant of time, velocities of its end point $A$ and centre $C$ are both perpendicular to the rod and opposite in direction, having magnitudes $11 \mathrm{m} {\mathrm{s}}^{-1}$ and $3 \mathrm{m} {\mathrm{s}}^{-1}$, respectively as shown in the figure.

The velocity of centre $C$ and angular velocity of the rod remain constant.

A force $F$ is applied on the top of a cube as shown in the figure. The coefficient of friction between the cube and the ground is $\mu .$ If $F$ is gradually increased, the cube will topple before sliding, if