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

A particle of mass $8 \mu \mathrm{~g}$ in motion collides with another stationary particle of mass $4 \mu \mathrm{~g}$. If the collision is perfectly elastic and one dimensional, the ratio of their de-Broglie wavelengths after collision is