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A tank is filled up to a height 2H with a liquid and is placed on a platform of height H from the ground. The distance x from the ground where a small hole is punched to get the maximum range R is

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1.25 H

1.5 H

answer is C.

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Detailed Solution

$As x = \frac{1}{2} {gt}^{2}; t = \sqrt{\frac{2 x}{g}}$

$Velocity of efflux v = \sqrt{2 g (3 H - x)}$

$Hence R = Vt = 2 \sqrt{x (3 H - x)}$

$For range to be maximum \frac{dR}{dx} = 0$

$Which gives x = \frac{3}{2} H$

$\Rightarrow x = 1.5 H$

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