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

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answer is 2.

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Detailed Solution

volume of cylinder $= V$

$ρ (\frac{3}{4} V) g = m g$

$V = \frac{4 m}{3 ρ}$

In reference frame of vessel

$m g - \frac{ρ}{4} V g_{e f f} - m A = m A / 3$

$g_{e f f} = g - A$

$m g - \frac{ρ}{4} (\frac{4 m}{3 ρ}) (g - A) - m A = m A / 3$ or $A = \frac{2 g}{3}$

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