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 :

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