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A solid floats in liquid A with half its...

A solid floats in liquid A with half its volume immersed and in liquid B with `2/3` of its volume immersed. The densities of the liquids A and B are in the ratio.

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Weight of liquid A displaced is `W_A = 1/2 V rho_A g`
Weight of liquid B displaced is `W_B = 2/3 rho_B g`
According to Archimede.s principle `W_A = W_B`
`1/2 V rho_A g = 2/3 V rho_B g`
`(rho_A)/(rho_B) = 4/3`
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