$A$ sphere of mass $0.1 \ kg$ is attached to a string of length $1 \ m$. It is released from a horizontal position and collides with another sphere of equal mass $m$ at rest. Find the kinetic energy gained by the second sphere. The collision is perfectly elastic. (in $J$)

$A$ ball of mass $m$ moving with a speed $u$ undergoes a head-on elastic collision with a ball of mass $nm$ initially at rest. The fraction of the incident energy transferred to the heavier ball is

$A$ light particle moving horizontally with a speed $v_1$ strikes a very heavy block moving in the same direction with a speed $v_2$. The collision is elastic. After the collision,the velocity of the particle is:

$A$ moving body with a mass $m_1$ and velocity $u$ strikes a stationary body of mass $m_2$. The masses $m_1$ and $m_2$ should be in the ratio $\frac{m_1}{m_2}$,so as to decrease the velocity of the first body to $\frac{2u}{3}$ and give a velocity of $v$ to $m_2$,assuming a perfectly elastic impact. Then,the ratio $\frac{m_1}{m_2}$ is

$A$ body falling on the ground from a height of $10 \, m$,rebounds to a height of $2.5 \, m$. The ratio of the velocities of the body just before and after the collision will be:

Statement-$1$: In an elastic collision between two bodies,the relative speed of the bodies after the collision is equal to the relative speed of the bodies before the collision.
Statement-$2$: In an elastic collision,the linear momentum of the system is conserved.