JEE Main 2016 · 9 Apr · Shift 1 · Physics Q7

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PhysicsSingle correct+4 / -1Question 7 of 90

Consider a water jar of radius R that has water filled up to height H and is kept on a stand 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 :

A jar of radius R filled to height H on a stand of height h; a stream of radius r leaves a hole at the bottom and narrows to radius x at the ground.

x=r\left(\dfrac H{H+h}\right)

x=r\left(\dfrac H{H+h}\right)^{1/2}

x=r\left(\dfrac H{H+h}\right)^{1/4}

x=r\left(\dfrac H{H+h}\right)^2

Answer and worked solution

Official answer: C

Leaving the hole, $v_1=\sqrt{2gH}$ ; at the ground, $v_2=\sqrt{2g(H+h)}$ . Continuity, $r^2v_1=x^2v_2$ , gives
$x=r\left(\frac H{H+h}\right)^{1/4}.$

Topics:Continuity equation Bernoulli's principle

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JEE Main 2016 · 9 Apr · Shift 1, Physics question 7