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

Let V be the volume of the block. When block floats in water, then `V_(rho "block") q= ((4)/(5)V) rho_("water")g`
or `rho_("block")=(4)/(5) rho_("water")` …(i)
When block floats in liquid. `v_(rho "block")g= Vrho_("liquid") g`
`rho_("block")= rho_("liquid")`
`rho_("liquid")= (4)/(5) rho_("water")` [from Eq (i)]
`=(4)/(5) xx 10^(3) kg m^(-3)`
=800kg `m^(-3)`