$A$ ball is dropped from height $h$ on a plane. If the coefficient of restitution of the plane is $e$ and the ball hits the ground two times,the height up to which it reaches after two jumps will be:

Collision takes place between two solid spheres denoted as $1$ and $2$. The initial velocities of the spheres are $u_1 = 3 \ m/s$ and $u_2 = 1.5 \ m/s$,and the final velocities are $v_1 = 2.5 \ m/s$ and $v_2 = 3.5 \ m/s$. The coefficient of restitution between the materials of the spheres is nearly:

Which one of the following statements does not hold good when two balls of masses $m_1$ and $m_2$ undergo elastic collision?

$A$ body of mass $m$ moving with a velocity $v$ collides head-on with another body of mass $2m$ at rest. If the coefficient of restitution between the two bodies is $e$,then the ratio of the velocities of the two bodies after collision is:

$A$ particle of mass $m$ moving with a velocity $u$ makes an elastic one-dimensional collision with a stationary particle of mass $m$. They are in contact for a total time $T$. The contact force increases linearly from $0$ to $F_0$ in time $\frac{T}{4}$, remains constant for a further time $\frac{T}{2}$, and decreases linearly from $F_0$ to $0$ in the final time $\frac{T}{4}$, as shown in the graph. The magnitude of $F_0$ is:

$A$ body of mass $m$ moving with velocity $v$ collides with a stationary body of mass $2m$. The fraction of kinetic energy lost by the body of mass $m$ is: