Question

A wooden block floating in a bucket of water has 4/5
of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is:-
(A) 0.5 (B) 0.7
(C) 0.6 (D) 0.8

Answer 1

$\huge\bold{(C)0.6}$

Answer 2

The density of oil relative to that of water is 0.6

given

4/5th of the volume of wooden block is submerged in water

so 4/5vρ(water)g=mg............(1)

second condition

v/2ρ(water)g+v/2ρ₀g=mg

from 1 and 2 we get

4/5vρ(water)g=v/2ρ(water)g+v/2ρ₀g

4/5ρ(water)=ρ(water)/2+ρ₀/2

(4/5-1/2)ρ(water)=ρ₀/2

thereforeρ₀/ρ(water)=3/5=0.6