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The shape of an ancient water clock jar is such that the water level descends at a constant rate at all times. The water level falls by $λ m / s$ and the shape of the jar is given by $y α x^{n} .$ Find the value of n if the radius r of the drain hole can be assumed to be very small.

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answer is 4.

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Detailed Solution

$a \sqrt{2 g y} = (π x^{2}) (- \frac{d y}{d t})$

$- \frac{d y}{d t} =$ constant $\Rightarrow y = \propto x^{4}$

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