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

A batsman hits a ball of mass 0.2 kg straight towards the bowler without changing its initial speed of $$6 \mathrm{~m} / \mathrm{s}$$. What is the impulse imparted to the ball?

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