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A uniform solid cylinder of density 0.8 \mathrm{~g} / \mathrm{cm}^3 floats in equilibrium in a combination of two non-mixing liquid A and B with its axis vertical. The densities of liquid A and B are \mathrm{0.7 \mathrm{~g} / \mathrm{cm}^3} and 1.2 \mathrm{gm} / \mathrm{cm}^3. The height of liquid A is \mathrm{h_A=1.2 \mathrm{~cm}} and the length of the part of cylinder immersed in liquid B is \mathrm{h_B=0.8 \mathrm{~cm}.} Then the length of the cylinder in air is

Option: 1

0.21 m


Option: 2

0.25 cm


Option: 3

0.35 cm


Option: 4

0.4 cm


Answers (1)

best_answer

\mathrm{\begin{aligned} & \mathrm{P}_{\mathrm{A}}(1.2 \times 0.7 \times \mathrm{g}+0.8 \times 1.2 \mathrm{~g}) \\ & 0.8 \times \mathrm{A}_0(\mathrm{x}+1.2+0.8) \mathrm{g}= \\ & \mathrm{x}+1.2+0.8=0.84+0.96 \\ & \mathrm{x}=0.25 \mathrm{~cm} \end{aligned}}

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Rishabh

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