A molecule of mass 'm' moving with velocity 'v' makes 5 elastic collisions with a wall of container per second. The change in momentum of the wall per second in 5 collisions will be

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

A bullet of mass $$m$$ moving with velocity $$v$$ is fired into a wooden block of mass $$M$$, If the bullet remains embedded in the block, the final velocity of the system is