A solid cylinder of mass $M$ and radius $R$ rolls without slipping down an inclined plane of length $L$ and height $h$. What is the speed of its centre of mass when the cylinder reaches its bottom?

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:-

The diagram shows the velocity-time graph for two masses $R$ and $S$ that collided elastically. Which of the following statements is true?

I. $R$ and $S$ moved in the same direction after the collision

II. The velocities of $R$ and $S$ were equal at the mid time of the collision.

III. The mass of $R$ was greater than mass of $S$.

The system of two blocks $A$ and $B$ are connected by an inextensible massless strings as shown. The pulley is massless and frictionless. Initially the system is at rest when, a bullet of mass '$\mathrm{m}$' moving with a velocity '$\mathrm{u}$' as shown hits the block '$B$' and gets embedded into it. The impulse imparted by tension force to the block of mass $3 \mathrm{m}$ is-