A particle of mass '$$m$$' collides with another stationary particle of mass '$$M$$'. A particle of mass '$$\mathrm{m}$$' stops just after collision. The coefficient of restitution is

Two masses '$$m_{\mathrm{a}}$$' and '$$\mathrm{m}_{\mathrm{b}}$$' moving with velocities '$$v_{\mathrm{a}}$$' and '$$v_{\mathrm{b}}$$' opposite directions collide elastically. Alter the collision '$$m_a$$' and '$$m_b$$' move with velocities and '$$v_{\mathrm{b}}$$' and '$$v_a$$' respectively, then the ratio $$\mathrm{m_a:m_b}$$ is

In system of two particles of masses $m_1$ and $m_2$, the first particle is moved by a distance $d$ towards the centre of mass. To keep the centre of mass unchanged, the second particle will have to be moved by a distance

$N$ number of balls of mass $m \mathrm{~kg}$ moving along positive direction of $X$ - axis, strike a wall per second and return elastically. The velocity of each ball is $u \mathrm{~m} / \mathrm{s}$. The force exerted on the wall by the balls in newton, is