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