Two balls each of mass 250 g moving in opposite directions each with a speed $16 \mathrm{~ms}^{-1}$ collide and rebound with the same speeds. The impulse imparted to one ball due to the other is

A block of mass 10 kg moving with a speed of $5 \hat{\mathrm{i}} \mathrm{ms}^{-1}$ on a frictionless horizontal surface suddenly explodes into two pieces. If one piece with mass 4 kg moves with a speed of $10 \hat{\mathbf{i}} \mathrm{~ms}^{-1}$, then the velocity of the second piece is

A steel sphere of radius 1.2 cm collides a second steel sphere at rest. If the collision is elastic and after the collision the first sphere continues to move in its initial direction with a velocity of $\frac{7}{9}$ times its initial velocity, then the radius of the second sphere is

If two bodies of masses 2 kg and 3 kg are moving at right angles with velocities $20 \mathrm{~ms}^{-1}$ and $10 \mathrm{~ms}^{-1}$ respectively, then the velocity of the centre of mass of the system of the two bodies is