A small body of superdense material, whose mass is twice the mass of the Earth but whose size is very small compared to the size of the Earth, starts from rest at a height $\mathrm{H}<<\mathrm{R}$ above the Earth's surface, and reach the, Earth's surface in time $t$. Then $t$ is equal to

Find the distance between centre of gravity and centre of mass of a two particle system attached to the ends of a light rod. Each particle has the same mass. Length of the rod is $R$, where $\mathrm{R}$ is the radius of the Earth.

In an experiment with a 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 :-

A uniform $"L"$ shaped rigid body $AOB$ of mass $m,$ where $AO=OB=l$ and $\angle AOB$ is a right angle, is hinged to a smooth joint at point $A$ of the body and can swing freely in a vertical plane. Initially, the body is released from rest with $AB$ horizontal. Find the maximum kinetic energy of the body.

On a smooth carom board, a coin moving in negative $y$-direction with a speed of $3 \mathrm{m} {\mathrm{s}}^{-1}$ is being hit at the point $\left(4,6\right)$ by a striker moving along negative $x$-axis. The line joining centres of the coin and the striker just before the collision is parallel to $x$-axis. After collision the coin goes into the hole located at the origin. Masses of the striker and the coin are equal. Considering the collision to be elastic, the initial and final speeds of the striker in $\mathrm{m} {\mathrm{s}}^{-1}$ will be:-

Two men '$A$' and '$B$' are standing on a plank. '$B$' is at the middle of the plank and '$A$' is at the left end of the plank. Surface of the plank is smooth. System is initially at rest and masses are as shown in figure. $A$ and $B$ starts moving such that the position of '$B$' remains fixed with respect to ground then '$A$' meet '$B$'. Then the point where $A$ meets $B$ is located at:-