$A$ ball of mass $m$ moving with velocity $v$ undergoes an elastic collision with another ball of the same mass $m$ moving in the opposite direction with velocity $2v$. What will be their velocities after the collision?

An alpha-particle of mass $m$ undergoes a $1$-dimensional elastic collision with a nucleus of unknown mass $M$ at rest. It is scattered directly backwards,losing $64\%$ of its initial kinetic energy. The mass of the nucleus is .......... $m$.

$A$ ball hits the floor and rebounds. For this elastic collision case,which of the following is true?

$A$ body of mass $8 \ kg$ moving with a certain velocity collides elastically with another body of mass $2 \ kg$ at rest. If $E$ is the initial kinetic energy of the moving mass,what will be the remaining kinetic energy of the moving mass after the collision (in $E$)?

The bob $A$ of a pendulum released from $30^o$ to the vertical hits another bob $B$ of the same mass at rest on a table as shown in Figure. How high does the bob $A$ rise after the collision? Neglect the size of the bobs and assume the collision to be elastic.

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?