A cylindrical vessel filled with water upto a height h weighs w and is resting on a horizontal plane. The side wall of the vessel has a plugged circular hole touching the bottom. The coefficient of fr

Question

A cylindrical vessel filled with water upto a height h weighs w and is resting on a horizontal plane. The side wall of the vessel has a plugged circular hole touching the bottom. The coefficient of friction between the bottom of the vessel and the plane is μ . The minimum diameter of the hole so that the vessel just begins to move on the floor after the removal of the plug is

TestHub · Accepted Answer

The horizontal momentum flux of the water leaving the hole gives the reaction:
$F = ρ A v^{2}$
At the threshold of sliding, this equals the maximum friction:
$F = μ w$
$v^{2} = 2 g h$
$A = \frac{π D ^{2}}{4}$
Substitute:
$ρ \frac{π D ^{2}}{4} (2 g h) = μ w$
$D^{2} = \frac{2 μ w}{π ρ h g}$
$D = \frac{2 μ w}{π ρ h g}$
Option D.

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