Two masses $m_1$ and $m_2$ moving with velocities $V_1$ and $V_2$ in opposite directions collide elastically and after collision $m_1$ and $m_2$ move with velocities $V_2$ and $V_1$ respectively. The ratio $\frac{m_2}{m_1}$ is

Six identical balls are lined up in a straight groove on a horizontal frictionless surface. Two similar balls,each moving with a velocity $v$,collide elastically with the row of $6$ balls from the left. What will happen?

$A$ neutron makes a head-on elastic collision with a stationary deuteron. The fractional loss of energy of the neutron in this collision is:

$A$ body of mass $5\, kg$ moving with a velocity $10\, m/s$ collides with another body of mass $20\, kg$ at rest and comes to rest. The velocity of the second body due to the collision is ............ $m/s$.

$A$ neutron moving with velocity $u$ collides elastically with an atom of mass number $A$. If the collision is head-on and the initial kinetic energy of the neutron is $E$, then the final kinetic energy of the neutron after the collision is:

$A$ ball of mass $2m$ and a system of two balls with equal masses $m$ connected by a massless spring are placed on a smooth horizontal surface (see figure). Initially, the ball of mass $2m$ moves with velocity $u_0$ along the line passing through the centres of all the balls and the spring, whereas the system of two balls is at rest. Assuming that the collision between the individual balls is perfectly elastic, the ratio of vibrational energy stored in the system of two connected balls to the initial kinetic energy of the ball of mass $2m$ is