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The figure shows a hollow cube of side ‘a’ of volume V. There is a small chamber of volume $\frac{V}{4}$ in the cube as shown. This chamber is completely filled by m kg of water. Water leaks through a hole H. Then the work done by gravity in this process (assuming that the complete water finally at the bottom of the cube) is $\frac{5}{n} mga$ . The value of 'n' is

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answer is 8.

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Detailed Solution

Let h be the height of water surface, finally $a^{2} h = a \cdot \frac{a}{2} \cdot \frac{a}{2}; h = \frac{a}{4}$

$∴$ C.M. gets lowered by $a - (\frac{a}{4} + \frac{a}{8}) = a - \frac{3a}{8} = \frac{5a}{8}$

$∴$ Work done by gravity = mg $\frac{5a}{8}$

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