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
  $x = r\left( \frac{H}{H + h} \right)^{\frac{1}{4}}$
• B
  $x = r\left( \frac{H}{H + h} \right)$
• C
  $x = r\left( \frac{H}{H + h} \right)^2$
• D
  $x = r\left( \frac{H}{H + h} \right)^{\frac{1}{2}}$