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Two small balls A and B of mass M and 3M hang from the ceiling by strings of equal length. The ball A is drawn a side so that it is raised to a height H. It is then released and collides with ball B. Select the correct answer (s).

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If the collision is perfectly inelastic, the combined mass will rise to a height

\frac{H}{16}

If the collision is perfectly elastic ball A will rise up to a height

\frac{H}{4}

If collision is perfectly elastic, ball B will rise to a height

\frac{H}{4}

If the collision is perfectly inelastic, the combined mass will rise to a height

\frac{H}{4}

answer is A, B, C.

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Detailed Solution

Before collision

$u_{1} = \sqrt{2gh} u_{2} = 0$

$v_{C} = \frac{m \sqrt{2gh} + 0}{m + 3 m} = \frac{\sqrt{2gh}}{4}$

$h_{max} = \frac{u^{2}}{2g} = \frac{2gh}{4 \times 2g} = \frac{H}{4}$

Both A and B raise to a height of $\frac{H}{4}$

If inelastic collision.

$\frac{1}{2} (m + 3 m) v_{C}^{2} = mgh$

$\frac{1}{2} \times 4 m \times {(\frac{\sqrt{2gh}}{4})}^{2} = 4 mgh$

$h = \frac{H}{16}$

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