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 :

Question

$\begin{array}{1 1}(1)x= r \bigg[\large\frac{H}{H+h}\bigg]^2 \\(2)x= r \bigg[\large\frac{H}{H+h}\bigg] \\ (3)x= r \bigg[\large\frac{H}{H+h}\bigg]^{\large\frac{1}{4}} \\ (4)x= r \bigg[\large\frac{H}{H+h}\bigg]^{\large\frac{1}{2}} \end{array} $