A solid cylinder of height \( h \) and mass \( \mathrm{m} \) floats in a liquid of density \( \r...

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A solid cylinder of height \( h \) and mass \( \mathrm{m} \) floats in a liquid of density \( \rho \) as shown in figure. Now the cylinder is released inside a liquid of density \( \rho / 4 \), 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) \( \frac{2}{3} g \)
(b) \( \frac{4}{3} g \)
(c) \( \frac{3}{4} g \)
(d) \( \frac{1}{3} g \)
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