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 $\left(\mathrm{r}<<\mathrm{R}\right)$ 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:

• Correct answer
  A

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

  $\mathrm{x}=\mathrm{r}\left(\frac{\mathrm{H}}{\mathrm{H}+\mathrm{h}}\right)$
• C

  $\mathrm{x}=\mathrm{r}{\left(\frac{\mathrm{H}}{\mathrm{H}+\mathrm{h}}\right)}^2$
• D

  $\mathrm{x}=\mathrm{r}{\left(\frac{\mathrm{H}}{\mathrm{H}+\mathrm{h}}\right)}^{\frac{1}{2}}$

Hence, the correct answer is option: 'A'.