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

$A$ smooth sphere $A$ is moving on a frictionless horizontal plane with angular speed $\omega$ and center of mass with velocity $v$. It collides elastically and head-on with an identical sphere $B$ at rest. Neglect friction everywhere. After the collision,their angular speeds are $\omega_A$ and $\omega_B$ respectively. Then

$A$ ball of mass $m$ moving with speed $u$ undergoes a head-on elastic collision with a stationary ball of mass $nm$. What is the fraction of the kinetic energy transferred to the heavier ball?

$Assertion$ : If collision occurs between two elastic bodies,their kinetic energy decreases during the time of collision.
$Reason$ : During collision,intermolecular space decreases and hence elastic potential energy increases.

$A$ ball after falling from a height of $10 \ m$ strikes the roof of a lift which is descending with a velocity of $1 \ m/s$. The recoil velocity of the ball will be ............. $m/s$. (Assume elastic collision)