Cosider a gravity - free hall in which a tray of mass M , carrying a cubical block of ice of mass m and edge L , is at rest in the middle. If the ice melts, by what distance does the centre of mass of "the tray plus the ice" system descent ?

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zero

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Solution

The correct option is C
zero

$X_{c m}$ = $\frac{m_{1} X_{1} + m_{2} X_{2}}{m_{1} + m_{2}}$ = 0
But as there is no gravity , the shape of ice even when it melts completely, will remain the same.
Therefore , COM will not move.
This can be concluded that in absemce of net external force on any system its COM does not change its sate with time.

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