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 Bernoulli's theorem, the velocity of water at point A \[\upsilon =\sqrt{2gh}\] 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\[R=\upsilon t\]                 \[=\sqrt{2gh}\times \sqrt{\frac{2(H-h)}{g}}\]                 \[=2\sqrt{(H-h)h}\]