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 $\mu$. 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. $\frac{\mu M}{\rho h}$
• B. $\frac{\sqrt{2\mu M}}{\rho h}$
• C. $\frac{\mu M}{2\rho h}$
• D. None of these

Answer 1

The correct option is C $\frac{\mu M}{2\rho h}$

$\begin{array}{c}\mu \left[\rho Ahg\right]=\frac{dM}{dt}.V\\ \Rightarrow \mu \left[\rho Ahg\right]=\rho .av.v\\ \Rightarrow \mu Ahg=a{v}^2\\ \Rightarrow a=\frac{\mu Ahg}{v^2}\\ \Rightarrow a=\frac{\mu Ahg}{2gh}\\ =\frac{\mu A}{2}\\ =\frac{\mu Ah\rho }{2h\rho }\\ =\frac{\mu M}{2\rho h}\\ Hence,theoptionCisthecorrectanswer.\end{array}$