Consider a water jar of radius R that has water filled up to height H… | JEE Main 2016 (9 Apr, Shift 1)

Q25JEE Main 2016 · 9 APR · SHIFT 1Difficult

Velocity of Efflux (Torricelli)

Consider a water jar of radius R that has water filled up to height H and is kept on astand of height h (see figure). Through a hole of radius r (r << R) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is x. Then:

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Answer: (c)

Speed at the hole: $v_1 = \sqrt{2gH}$ ; speed at the ground: $v_2 = \sqrt{2g(H+h)}$ .
Continuity: $\pi r^2 v_1 = \pi x^2 v_2 \Rightarrow x^2 = r^2\sqrt{\frac{H}{H+h}}$
So the answer is (c) $x = r\left(\frac{H}{H+h}\right)^{1/4}$ .

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Velocity of Efflux (Torricelli) question from JEE Main 2016 (9 Apr, Shift 1)

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