A body floats with $1 / 3$ of its volume outside when immersed in water. The same body floats with $3 / 4$ of its volume inside when immersed in some other liquid. The density of the other liquid in $g c m^{- 3}$ is (density of water $= 1000 k g / m^{3}$ )

\frac{8}{9}

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\frac{9}{4}

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\frac{8}{3}

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\frac{4}{9}

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Solution

The correct option is C $\frac{8}{3}$
We know that, $B = V_{p g}$

When the body floats $1 / 3$ of its volume outside when immersed in water.
Upthrust (Weight of liquid displaced) = Weight of body.

$\frac{2}{3} V_{p W g} = V_{p g} \dots (i)$

When the body floats $3 / 4$ of its volume inside when immersed in some other liquid.
Upthrust (Weight of liquid displaced) = Weight of body.

$\frac{1}{4} V_{p L g} = V_{p g} \dots (i i)$

From (𝑖) and (𝑖𝑖),

$\frac{2}{3} V_{p W g} = \frac{1}{4} V_{p L g}$

$\frac{8}{3} p_{W} = p_{L}$

$p_{L} = \frac{8}{3} g m / c m^{3}$

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A body floats with 1/3 of its volume outside when immersed in water. The same body floats with 3/4 of its volume inside when immersed in some other liquid. The density of the other liquid in gcm−3 is (density of water =1000 kg/m3)

A body floats with $1 / 3$ of its volume outside when immersed in water. The same body floats with $3 / 4$ of its volume inside when immersed in some other liquid. The density of the other liquid in $g c m^{- 3}$ is (density of water $= 1000 k g / m^{3}$ )