Four particles $A, B, C$ and $D$ of equal mass are placed at four corners of a square. They move with equal uniform speed $v$ towards the intersection of the diagonals. After collision, $A$ comes to rest, $B$ traces its path back with same speed and $C$ and $D$ move with equal speeds. What is the velocity of $C$ after collision
$\frac{2v}{3}$
$2\,v$
$\frac{v}{2}$
$v$
A mass of $0.5\, kg$ moving with a speed of $1.5\, m/s$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant $k=50\,N/m$. The maximum compression of the spring would be ................. $\mathrm{m}$
When a ball is freely fallen from a given height it bounces to $80\%$ of its original height. What fraction of its mechanical energy is lost in each bounce ?
The length of a spring is $\alpha $ when a force of $4\,N$ is applied on it and the length is $\beta $ when $5\,N$ force is applied. Then the length of spring when $9\,N$ force is applied is
$ABCDE$ is a channel in the vertical plane, part $BCDE$ being circular with radius $r$ . A block is released from $A$ and slides without friction and without rolling. The block will complete the loop if $h$ is
$A$ ball is projected from ground with a velocity $V$ at an angle $\theta$ to the vertical. On its path it makes an elastic collison with $a$ vertical wall and returns to ground. The total time of flight of the ball is