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 \[R=\upsilon t\] \[=\sqrt{2gh}\times \sqrt{\frac{2(H-h)}{g}}\] \[=2\sqrt{(H-h)h}\]