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A light cylindrical vessel is kept on a ...

A light cylindrical vessel is kept on a horizontal surface it's base area is `A`. A hole of cross-sectional area `a` is made just at it's bottom side. The minimum coefficient of friction necessary for not sliding of vessel due to the impact force of the emerging liquid.

A

varying

B

a/A

C

2a/A

D

None of these

Text Solution

Verified by Experts

The velocity of efflux of the liquid is given as
` v = sqrt (2gy)`
` :. ` The reaction force of the emerging liquid on the vessel + liquid content is equal to
`F = v (dm)/(dt) = varho v = a rho v^(2)`
`rArr F = a rho ( sqrt(2gy ))^(2) = 2 a rho gy`
` rArr muN = 2 a rho gy`
` rArr mu (A rho gy) = 2a rho gy`
` rArr mu = (2a)/A`
Hence (C ) is correct
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