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Q.

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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a

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

b

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

c

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

d

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

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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If water drops are falling at regular time intervals from ceiling of height H, then position of drop from the ceiling is (when nth drop falling from the ceiling and rth drop is in its way)