A block of wood floats in water with `(4//5)th` of its volume submerged. If the same block just floats in a liquid, the density of liquid in `(kg m^(-3))` is

Options

A. 1250
B. 600
C. 400
D. 800

Answer

D

Explanation

According to Archimede's principle
Weight of the body =Weight of the liquid displaced
let V be volume of block.
In water , `Vrho_("block")g=((4)/(5)V)rho_("water")g`
`rho_("block")=(4)/(5)rho_("water")" "…(i)`
In liquid, `Vrho_("block")g=Vrho_("liquid")g`
`rho_("block")=rho_(liquid")" "...(ii)`
From (i) and (ii), we get
`rho_("liquid")=(4)/(5)rho_("water")=(4)/(5) xx 10^(3) kg m^(-3)=800 kg m^(-3)`