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To what height h should a cylindrical vessel of diameter d be filled with a liquid so that the total force on the vertical surface of the vessel be equal to the force on the bottom-

A
h=d
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B
h=2d
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C
h=3d
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D
h=d/2
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Solution

The correct option is D h=d/2
If we fill the cylinder upto a height h, the force exerted on at the bottom of the cylinder would be equal to F = PA

F=ρgh×πd2/4

Similarly, the average force exerted along the sides of the cylinder will be because of half the height filled for the cylinder.

Therefore, F=ρgh/2×πdh

Equating the 2 forces, and solving for h, gives h = d/2

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