Consider a water jar of radius R that has water filled up to height...

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

\left(r < < R\right)

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:

Options

Ax = r{ $\left(\dfrac{H}{H + h}\right)}^{\dfrac{1}{4}}$
B $x = r\left(\dfrac{H}{H + h}\right)$
Cx = r{ $\left(\dfrac{H}{H + h}\right)}^{2}$
Dx = r{ $\left(\dfrac{H}{H + h}\right)}^{\dfrac{1}{2}}$

Correct answer

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

Step-by-step solution

Using equation of continuity

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

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

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