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 :
A
x=√D(H−D)
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B
x=√D(H−D)2
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C
x=2√D(H−D)
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D
x=4√D(H−D)
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Solution
The correct option is Cx=2√D(H−D) 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(H−D)g. Therefore, x=√2gD×√2(H−D)g=2√D(H−D). Hence, the horizontal distance x in terms of H and D is2√D(H−D).