If water drops are falling at regular time intervals from ceiling of height H, then position of drop from the ceiling is (when n^thdrop falling from the ceiling and r^th drop is in its way)

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$\frac{{(n - r)}^{2}}{{(n + 1)}^{2}} H$

$\frac{{(n + 1)}^{2}}{{(n + r)}^{2}} H$

$\frac{{(n - r)}^{2}}{{(n - 1)}^{2}} H$

$\frac{{(n - 1)}^{2}}{{(n - r)}^{2}} H$

answer is B.

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Detailed Solution

In the time 1st drop reaches ground nth drop starts to drop.

So, n-1 drops of water dropped in the given time.

H = ½ gT²

H_1st = ½ g(n-1)²

H_rth = ½ g(n-r)²

H_rth = $\frac{{(n - r)}^{2}}{{(n - 1)}^{2}} H$

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