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Question

A tank is filled with water up to height H. Water is allowed to come out of a hole P in one of the walls at a depth D below the surface of water as shown in the figure. Express the horizontal distance x in terms of H and D :
295512_e3b35e85b3074361b84ccce962ff1033.png

A
x=D(HD)
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B
x=D(HD)2
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C
x=2D(HD)
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D
x=4D(HD)
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Solution

The correct option is C x=2D(HD)
Answer is C.
The velocity of water stream coming out of P = 2gD.
The time taken by the water stream to fall through the height H-D = 2(HD)g.
Therefore, x=2gD×2(HD)g=2D(HD).
Hence, the horizontal distance x in terms of H and D is 2D(HD).

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