$A$ ball falling freely from a height of $4.9 \, m$ hits a horizontal surface. If the coefficient of restitution is $e = \frac{3}{4}$,then the ball will hit the surface for the second time after .............. $s$.

$A$ body of mass $m$ moving with velocity $v$ collides inelastically with another body of the same mass. After the collision,the first body moves with velocity $\frac{v}{\sqrt{3}}$ in a direction perpendicular to the initial direction of motion. What will be the speed of the second body after the collision?

$A$ body is dropped on the ground from a height $h_1$ and after hitting the ground,it rebounds to a height $h_2$. If the ratio of velocities of the body just before and after hitting the ground is $4$,then the percentage loss in kinetic energy of the body is $\frac{x}{4}$. The value of $x$ is $.......$

The sphere $A$ of mass $m$ moving with a constant velocity hits another sphere $B$ of mass $2m$ at rest. If the coefficient of restitution is $0.4$,the ratio of the velocities of the spheres $A$ and $B$ after collision is

$A$ ball falls freely from a height $h$ on a rigid horizontal plane. If the coefficient of restitution is $e$,then the total distance travelled by the ball before hitting the plane the second time is

An electron collides with a free molecule initially in its ground state. The collision leaves the molecule in an excited state that is metastable and does not decay to the ground state by radiation. Let $K$ be the sum of the initial kinetic energies of the electron and the molecule,and $p$ be the sum of their initial momenta. Let $K^{\prime}$ and $p^{\prime}$ represent the same physical quantities after the collision. Then,