Question

A solid cylinder of height h and mass m floats in a liquid of density ρ as shown in figure. Now the cylinder is released inside a liquid of density $\frac{\rho }{4}$, contained in a downward accelerated vessel. Determine the magnitude of acceleration of vessel, a, for which cylinder sinks with relative acceleration a/3 with respect to vessel. Neglect any dissipative force :

• A. $\frac{2}{3}\text{g}$
• B. $\frac{4}{3}\text{g}$
• C. $\frac{3}{4}\text{g}$
• D. $\frac{1}{3}\text{g}$

Answer 1

Answer: (A)

$\frac{2}{3}\text{g}$

$\text{Volume of cylinder}=\text{V}\rho \left(\frac{3}{4}\text{V}\right)\text{g}=\text{mg}\text{V}=\frac{\text{4m}}{3\rho }\text{In reference frame of vessel}\text{mg}-\frac{\rho }{4}\text{V}{\text{g}}_{eff}-\text{mA}=\frac{mA}{3}{\text{g}}_{eff}=g-A\text{mg}-\frac{\rho }{4}\left(\frac{4\text{m}}{3\rho }\right)\left(\text{g-A}\right)-\text{mA}=\frac{\text{mA}}{3}\text{or}\text{A}=\frac{2\text{g}}{3}$