question_answer

A tank is filled with water upto height H. When a hole is made at a distance h below the level of water, what will be the horizontal range of water jet?

A)  \[2\sqrt{h(H-h)}\]          

B)         \[4\sqrt{h(H+h)}\]                         

C)         \[4\sqrt{h(H-h)}\]          

D)         \[2\sqrt{h(H+h)}\]

Correct Answer: A

Solution :

Applying Bernoullis theorem, the velocity of water at point\[A\]                 \[v=\sqrt{2\,\,gh}\] Time taken to reach point \[C\] is\[t\] So,          \[H-h=\frac{1}{2}g{{t}^{2}}\]                       \[t=\sqrt{\frac{2(H-h)}{g}}\] Now, horizontal range\[R=vt\]                 \[\sqrt{gh}\times \sqrt{\frac{2(H-h)}{g}}\]                 \[=2\sqrt{(H-h)}h\]