Two masses $\left(M\right)$ are moving perpendicular to the rod of mass $M$ with velocities $v\text{ and} 2v$ as shown in the figure. The length of the rod is $L$. Find the ratio of the final velocity of the rod and its angular velocity if the masses stop at their place after collision.

A uniform cube of mass $m$ and side $a$ is placed on a frictionless horizontal surface. A vertical force, $F=\frac{mg}{4}$ is applied to the edge as shown in figure. The normal reaction effectively acts at a distance,

A homogenous block having its cross-section to be a parallelogram of sides $a$ and $b$ (as shown) is lying at rest and is in equilibrium on a smooth horizontal surface. Then for acute angle $\mathrm{\theta }$:

In an experiment with a light beam balance, an unknown mass $m$ is balanced by two known masses of $16 \mathrm{kg}$ and $4 \mathrm{kg}$ as shown in figure. The value of the unknown mass $m$ is