A thin circular coin of mass $5 \mathrm{gm}$ and radius $\frac{4}{3} \mathrm{cm}$ is initially in a horizontal $xy$-plane. The coin is tossed vertically up ($+z$ direction) by applying an impulse of $\sqrt{\frac{\mathrm{\pi }}{2}}\times {10}^{-2} \mathrm{N}-\mathrm{s}$ at a distance $\frac{2}{3} \mathrm{cm}$ from its center. The coin spins about its diameter and moves along the $+z$ direction. By the time the coin reaches back to its initial position, it completes $n$ rotations. The value of $n$ is _____.

[Given: The acceleration due to gravity $g=10 \mathrm{m} {\mathrm{s}}^{-2}$]

A cubical block of side $30 \mathrm{cm}$ is moving with velocity $2 \mathrm{m} {\mathrm{s}}^{-1}$ on a smooth horizontal surface. The surface has a bump at a point $O$ as shown in the figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is :

Two thin circular discs of mass $m$ and $4m$, having radii of $a$ and $2a$, respectively, are rigidly fixed by a massless, right rod of length $\mathcal{l}=\sqrt{24}a$ through their center. This assembly is laid on a firm and flat surface, and set rolling without slipping on the surface so that the angular speed about the axis of the rod is $\omega$ . The angular momentum of the entire assembly about the point $O$ is $\overrightarrow{L}$ (see the figure). Which of the following statement(s) is(are) true?

A particle of mass $2 \mathrm{kg}$ is on a smooth horizontal table and moves in a circular path of radius $0.6 \mathrm{m}$. The height of the table from the ground is $0.8 \mathrm{m}$. If the angular speed of the particle is $12\mathrm{ }\mathrm{rad}\mathrm{ }{\mathrm{s}}^{-1}$ , the magnitude of its angular momentum about a point on the ground right under the center of the circle is: