A solid cylinder of length l and cross-sectional area a/5 is immersed… | MHT CET 2025 (23 Apr, Shift 2)

Q6MHT CET 2025 · 23 APR · SHIFT 2Medium

Archimedes' Principle & Floatation

A solid cylinder of length $l$ and cross-sectional area $\frac{a}{5}$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $l/4$ in the denser liquid as shown in figure. The lower density liquid ( $\rho$ ) is open to atmosphere having pressure $P_0$ . The density d of solid cylinder is

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Answer: (b)

From the figure, the lower liquid has density $3\rho$ and the upper liquid $\rho$ ; the cylinder has $l/4$ in $3\rho$ and $3l/4$ in $\rho$ .
Weight = upthrust: $d\,A l g = 3\rho\,A\dfrac{l}{4} g + \rho\,A\dfrac{3l}{4} g$
$d = \dfrac{3\rho}{4} + \dfrac{3\rho}{4} = \dfrac{3}{2}\rho$
So the answer is (b) $\dfrac{3}{2}\rho$ .

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Archimedes' Principle & Floatation question from MHT CET 2025 (23 Apr, Shift 2)

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