Four-fifths of a cylindrical block of wood float inside a liquid. If the relative density of wood is 0.7, find the density of the fluid.

$875 k g / m^{3}$

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$775 k g / m^{3}$

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$700 k g / m^{3}$

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None of these

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Solution

The correct option is
A

$875 k g / m^{3}$

let V be the volume of the block.

Density of the block $= 0.7 \times 1000 k g / m^{3}$

Volume of the block under the liquid $= \frac{4}{5} V$

Weight of the body = weight of the liquid displaced (since body floats)

$V \times 700 \times g = \frac{4 V}{5} \times ρ \times g$

$ρ = 875 k g / m^{3}$

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Four-fifths of a cylindrical block of wood float inside a liquid. If the relative density of wood is 0.7, find the density of the fluid.

The correct option is A 875 kg/m3 let V be the volume of the block. Density of the block =0.7×1000 kg/m3 Volume of the block under the liquid =45V Weight of the body = weight of the liquid displaced (since body floats) V×700×g=4V5×ρ×g ρ=875 kg/m3