# 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 : Option 1) Option 2) Option 3) Option 4)

As we learnt in

Equation of Continuity -

Mass of the liquid entering per second at A = mass of the liquid leaving per second at B.

a1 v1 = a2 v2

- wherein

a1  and abe the area of cross section.

A1v1 = A2v2

$\pi r^{2}\sqrt{2gH}=\pi x^{2}\sqrt{2g(H+h)}$

$\therefore\ \;x=r\left(\frac{H}{H+h} \right )^{1/4}$

Correct option is 3.

Option 1)

This is an incorrect option.

Option 2)

This is an incorrect option.

Option 3)

This is the correct option.

Option 4)

This is an incorrect option.

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