$A$ ball $P$ moving with a speed of $v \ ms^{-1}$ collides directly with another identical ball $Q$ moving with a speed $10 \ ms^{-1}$ in the opposite direction. $P$ comes to rest after the collision. If the coefficient of restitution is $0.6$,the value of $v$ is (in $ms^{-1}$)

$A$ ball moving with a velocity $v$ collides head-on with a stationary second ball of the same mass. After the collision,the velocity of the first ball is reduced to $0.15 v$. The kinetic energy of the system is decreased nearly by (in $\%$)

$A$ bullet of mass $0.01\, kg$ travelling at a speed of $500\, m/s$ strikes and passes horizontally through a block of mass $2\, kg$ which is suspended by a string of length $5\, m$. The centre of gravity of the block is found to rise a vertical distance of $0.1\, m$. What is the speed of the bullet after it emerges from the block? (The time of passing of the bullet is negligible,$g = 9.8\, m/s^2$)

During an inelastic collision between two objects,which of the following quantities always remains conserved?

$A$ particle of mass $m_1$ moving along the $X$-axis collides with a stationary particle of mass $m_2$ and deviates by an angle $30^{\circ}$ to the $X$-axis as shown in the figure. If the percentage change in kinetic energy of the combined system of these two particles reduces by $50 \%$,then the ratio of the masses $\frac{m_2}{m_1}$ is

$A$ smooth sphere is moving on a horizontal surface with a velocity vector $(2 \hat{i} + 2 \hat{j}) \ m/s$ immediately before it hits a vertical wall. The wall is parallel to the vector $\hat{j}$ and the coefficient of restitution between the sphere and the wall is $e = 1/2$. The velocity of the sphere after it hits the wall is: