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A hollow cylindrical container floats in water with half its length immersed. A liquid of specific gravity $σ$ is slowly poured into the container until the levels of the liquid inside the container and of water outside are the same. It is observed that the container is submerged to two-thirds its length. Then the value of $σ$ is

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$\frac{1}{5}$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{4}$

answer is C.

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Detailed Solution

For balancing the Weight of poured fluid the cylinder get more immersed than before so increase buoyant force,
Thus, weight of fluid poured = Increase in buoyant force

${σπr}^{2} \frac{2 h}{3} g = {πr}^{2} \frac{h}{6} \times 1 \times g$

$\Rightarrow σ = \frac{1}{4}$

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