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 .......... $m$.

Two masses $m_1$ and $m_2$ moving with velocities $V_1$ and $V_2$ in opposite directions collide elastically and after collision $m_1$ and $m_2$ move with velocities $V_2$ and $V_1$ respectively. The ratio $\frac{m_2}{m_1}$ is

$A$ ball after falling from a height of $10\, m$ strikes the roof of a lift which is descending down with a velocity of $1\, m/s$. The recoil velocity of the ball will be .............. $m/s$.

$A$ body of mass $30 \ kg$ moving with a velocity $20 \ ms^{-1}$ undergoes a one-dimensional elastic collision with another ball of the same mass moving in the opposite direction with a velocity of $30 \ ms^{-1}$. After the collision,the velocities of the first and second bodies respectively are:

$A$ body of mass $m$ moving with velocity $v$ makes a head-on collision with another body of mass $2m$ which is initially at rest. What is the ratio of the kinetic energy of the colliding body before and after the collision (in $: 1$)?

Consider an elastic collision of a particle of mass $m$ moving with velocity $u$ with another particle of the same mass $m$ at rest. After the collision, the particles move at angles $\theta_1$ and $\theta_2$ with respect to the initial direction of motion. What is the sum of the angles $\theta_1 + \theta_2$ in degrees?