$A$ ball of mass $m$ moving with velocity $V$ makes a head-on elastic collision with a ball of the same mass moving with velocity $2V$ towards it. Taking the direction of $V$ as positive,the velocities of the two balls after the collision are:

$A$ particle of mass $m$ is moving with a horizontal speed of $6 \, m/s$ as shown in the figure. If $m << M$,then for a one-dimensional elastic collision,the speed of the lighter particle after the collision will be:

$Assertion$ : 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.

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:

$A$ 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 $J$)

$A$ smooth sphere $A$ is moving on a frictionless horizontal plane with an angular velocity $\omega$ and its center of mass is moving with a linear velocity $v$. It undergoes an elastic collision with a stationary sphere $B$. (Ignore friction everywhere). If the angular speeds after the collision are $\omega_A$ and $\omega_B$ respectively,then: