$A$ body moving along a straight line collides with another body of the same mass moving in the same direction with half of the velocity of the first body. If the coefficient of restitution between the two bodies is $0.5$,then the ratio of the velocities of the two bodies after collision is (treat the collision as one dimensional).

$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ particle of mass $m$ strikes the rod at one end with a velocity $v$ perpendicular to the rod. If the particle comes to rest after the collision,the velocity of the center of mass of the rod after the collision is:

$A$ body of mass $m_1$ moving with a velocity $3 \, ms^{-1}$ collides with another body at rest of mass $m_2$. After the collision,the velocities of the two bodies are $2 \, ms^{-1}$ and $5 \, ms^{-1}$ respectively along the direction of motion of $m_1$. The ratio $\frac{m_1}{m_2}$ is:

$A$ ball of mass $2 \ g$ moving with a velocity of $2 \ ms^{-1}$ collides with another ball of mass $8 \ g$ which is at rest and comes to rest after collision. Then the coefficient of restitution is

$A$ tennis ball hits the floor with a speed $v$ at an angle $\theta$ with the normal to the floor. If the collision is inelastic and the coefficient of restitution is $\varepsilon$, what will be the angle of reflection?

$A$ particle of mass $m$ moving with speed $2v$ collides with a mass $2m$ moving with speed $v$ in the same direction. After the collision,the first mass is stopped completely,while the second one splits into two particles each of mass $m$,which move at an angle of $45^o$ with respect to the original direction. The speed of each of the moving particles will be: