A body of mass $M$ as shown in figure with a small disc of mass $m$ place on it rests on a smooth horizontal plane. The disc is set in motion in the horizontal direction with velocuity $ν$ . To what height (relative to the initial level) will the disc rise after breaking off the body $M$ ? The friction is assumed to be absent.

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$h = \frac{m ν^{2}}{3 (m + M) g}$

$h = \frac{3 m ν^{2}}{(m + M) g}$

$h = \frac{m ν^{2}}{2 (m + M) g}$

$h = \frac{2 m ν^{2}}{(m + M) g}$

answer is D.

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Detailed Solution

Applying the law of conservation of momentum

$m ν = (m + M) ν_{1} ν_{1} = \frac{m ν}{m + M}$

where $ν_{1}$ is the velocity of the combined system

Let disc rises to a height $h$ , then

$\frac{1}{2} m ν^{2} = m g h + \frac{1}{2} (m + M) ν_{1}^{2}$

Substituting the value of $ν_{1}$ , we get

$h = \frac{m ν^{2}}{2 (m + M) g}$

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