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Question

A cylindrical vessel is filled with a liquid of density 'p' upto height 'h' and placed on a horizontal surface. Coefficient of friction between the vessel and surface is μ. What should be the minimum area of a hole near the bottom of the vessel so that when the hole is unplugged, vessel begins to move? Mass of vessel and liquid is 'M'

A
μMρh
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B
2μMρh
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C
μM2ρh
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D
None of these
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Solution

The correct option is C μM2ρh
μ[ρAhg]=dMdt.Vμ[ρAhg]=ρ.av.vμAhg=av2a=μAhgv2a=μAhg2gh=μA2=μAhρ2hρ=μM2ρhHence,theoptionCisthecorrectanswer.

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