Question

A block of wood floats in water with $$\displaystyle \left ( \frac{4}{5} \right ) ^{th}$$ of its volume submerged. If the same block just floats in a liquid, the density of the liquid (in kg m$$^{-3}$$) is:

A
1250
B
600
C
400
D
800

Solution

The correct option is D 800According to Archimede's principle Weight of the body = Weight of the liquid displaced Let $$V$$ be volume of block.In water, $$\displaystyle V\rho _{block} g = \left ( \frac{4}{5}V \right ) \rho_{water}g$$$$\displaystyle \rho _{block} = \frac {4}{5} \rho _{weter}$$      ....(i)In liquid, $$\displaystyle V\rho_{block}g= V\rho _{liquid} g$$$$\displaystyle \rho _{block} =\rho _{liquid}$$                       .....(ii)From (i) and (ii), we get$$\displaystyle \rho _{Liquid}=\frac{4}{5} \rho_{water} = \frac{4}{5} \times 10^3\,kg\,m^{-3} = 800\,kg\,m^{-3}$$Physics

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