question_answer

A tank is filled with water up to 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 :

Account to Bernoulli theorem, The velocity of water at point A             \[V=\sqrt{2gh}\] If time taken (flight time) to reach point C is t Then,       \[H-h=\frac{1}{2}g{{t}^{2}}\]             \[t=\sqrt{\frac{2(H-h)}{g}}\] Now, horizontal range, R = velocity \[\times \] flight time             \[\Rightarrow \]            \[R=V\times t=\sqrt{2gh}\times \sqrt{\frac{2(H-h)}{g}}\]             \[\Rightarrow \]            \[R=2\sqrt{(H-h)}h\]