A body of mass $2\,kg$ makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body? ................ $ \mathrm{kg}$

$A$ chain of length $L$ and mass $m$ is placed upon a smooth surface. The length of $BA$ is $L-b$. Calculate the velocity of the chain when its end reaches $B$.

A billiard table whose length and width are as shown in the figure. $A$ ball is placed at point $A$. At what angle ‘$\theta $ ’the ball be projected so that after colliding with two walls, the ball will fall in the pocket $B$ .Assume that all collisions are perfectly elastic (neglect friction)

Three particles each of mass $m$ are located at the vertices of an equilateral triangle $ABC$. They start moving with equal speeds $v$ each along the medians of the triangle and collide at its centroid $G$. If after collision, $A$ comes to rest and $B$ retraces its path along $GB,$ then $C$

A particle of mass $m$ is moving with speed $2\, v$ collides with a mass $2\,m$ moving with speed $v$ in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass $m$, which move at angle $45^o$ with respect to the original direction. The speed of each of the moving particle will be

In figure, determine the type of the collision The masses of the blocks, and the velocities before and after the collision are given. The collision is