Hail storms are observed to strike the surface of the frozen lake at $30^o$ with the vertical and rebound at $60^o$ with the vertical. Assume contact to be smooth, the coefficient of restitution is

Two masses $m_1$ and $m_2$ are connected by a string of length $l$. They are held in a horizontal plane at a height $H$ above two heavy plates $A$ and $B$ made of different material placed on the floor. Initially distance between two masses is $a < l$. When the masses are released under gravity they make collision with $A$ and $B$ with coefficient of restitution $0.8$ and $0.4$ respectively. The time after the collision when the string becomes tight is :- (Assume $H>>l$)

A ball $P$  collides with another identical ball  $Q$  at rest. For what value of coefficient of restitution $e$ , the  velocity of ball  $Q$  become two times that of ball  $P$  after collision

The force constant of a wire is $k$ and that of another wire is $2k$. When both the wires are stretched through same distance, then the work done

Blocks of masses $m , 2 m , 4 m$ and $8 m$ are arranged in a line on a frictionless floor. Another block of mass $m ,$ moving with speed $v$ along the same line (see figure) ollides with mass $m$ in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass $8 m$ starts moving the total energy loss is $p \%$ of the original energy. Value of $'p'$ is close to

A mass $'m'$ moves with a velocity $'v'$ and collides inelastically with another identical mass. After collision the $1^{st}$ mass moves with velocity $\frac{v}{{\sqrt 3 }}$ in a direction perpendicular to the initial direction of motion. Find the speed of the $ 2^{nd}$ mass after collision