Particle $A$ makes a perfectly elastic collision with another particle $B$ at rest. They fly apart in opposite directions with equal speeds. If their masses are $m_A$ and $m_B$ respectively,then:

$A$ body of mass $5 \ kg$ makes an elastic collision with another body at rest and continues to move in the original direction after collision with a velocity equal to $\frac{1}{10}$ th of its original velocity. Then the mass of the second body is (in $kg$)

Consider the following statements $A$ and $B$ and identify the correct answer:
$A$. In an elastic collision,if a body suffers a head-on collision with another of the same mass at rest,then the first body comes to rest while the other starts moving with the velocity of the first one.
$B$. Two bodies of equal mass suffering a head-on elastic collision merely exchange their velocities.

Consider an elastic collision of a particle of mass $m$ moving with a velocity $u$ with another particle of the same mass at rest. After the collision, the projectile and the struck particle move in directions making angles $\theta_1$ and $\theta_2$ respectively with the initial direction of motion. The sum of the angles, $\theta_1 + \theta_2$, is equal to: (in $^\circ$)

Consider the situation as shown in the figure. The ball strikes the wall normally and the collision is elastic. The wall is moving with a velocity of $20 \ m/s$ to the right,and the ball is moving with a velocity of $10 \ m/s$ to the left. The mass of the ball is $500 \ g$. The change in the kinetic energy of the ball is $....J$.

$A$ point mass $M$ moving with a certain velocity collides with a stationary point mass $M / 2$. The collision is elastic and in one-dimension. Let the ratio of the final velocities of $M$ and $M / 2$ be $x$. The value of $x$ is