Two equal masses ${m_1}$ and ${m_2}$ moving along the same straight line with velocities $+ 3 \,m/s$ and $-5\, m/s$ respectively collide elastically. Their velocities after the collision will be respectively

A body falls on a surface of coefficient of restitution $0.6 $ from a height of $1 \,m$. Then the body rebounds to a height of ...........  $m$

In a collinear collision, a particle with an initial speed $v_0$ strikes a stationary particle of the same mass. If the final total kinetic energy is $50\%$ greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is:

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

A ball is dropped from a height of $20\,m$. If the coefficient of restitution for the collision between ball and floor is $0.5$, after hitting the floor, the ball rebounds to a height of $.............m$.

Blocks of masses $m , 2 m , 4 m$ and $8 m$ are arranged in a line on a frictionless floor. Another block of mass $m ,$ moving with speed $v$ along the same line (see figure) ollides with mass $m$ in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass $8 m$ starts moving the total energy loss is $p \%$ of the original energy. Value of $'p'$ is close to