Question

A wooden cylinder of diameter $4r$, height $H$ and density $\rho /3$ is kept on a hole of diameter $2r$ of a tank, filled with a liquid of density $\rho$ as shown in the figure.
If the level of the liquid starts decreasing slowly when the level of the liquid is at height $h_1$ above the cylinder the block starts moving up. At what value of $h_1$, will the block rise?

• A. $\frac{4H}{9}$
• B. $\frac{5H}{9}$
• C. $\frac{5H}{3}$
• D. Remains same

Answer 1

The correct option is C $\frac{5H}{3}$

$\begin{array}{c}\left[P_0+\rho g{h}_1\right]\pi \left(4r^2\right)+\frac{\rho }{3}\pi 4r^{2}hg\\ =\left[P_0+\rho g\left(h_1+h_2\right)\right]\pi \left(3r^2\right)+P_0\pi r^2\\ h_1=\frac{5h}{3}\\ Hence,theoptionCisthecorrectanswer.\end{array}$