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