question_answer

A vertical tank with depth H is full with water. A hole is made on one side of the walls at a depth h below the water surface. At what distance from the foot of the wall does the emerging stream of water strike the foot?

A) \[\sqrt{h(H-h)}\]

B) \[2\sqrt{h/(H-h)}\]

C) \[2(H-h)\sqrt{h/(H-h)}\]

D) \[\sqrt{2h/(H-h)}\]

Correct Answer: B

Solution :

Time taken by water to reach the foot \[t=\sqrt{\frac{2(H-h)}{g}}\] Velocity of water coming out of hole \[v=\sqrt{2gh}\] \[\therefore \] Emerging stream of water strike the foot \[x=v\times t\] \[=\sqrt{2gh}\times \sqrt{\frac{2(H-h)}{g}}\] \[=2\sqrt{h(H-h)}\]