Question

A body floats in water with 40% of its volume outside water. When this body is kept in oil, it
floats with 60% of its volume remains outside the oil. The relative density of oil is
k/2
Find value
of K.

Answer 1

Since the body is 60% submerged in water, it's density has to be 0.6 g/cc

Since the body remains 40% submerged in oil, the density of oil has to be 0.6/0.4=1.5 g/cc, which is weird since almost all oils have density less than water. But let's go ahead with the question.

Relative density = 1.5/1.0 = 1.5 = K/2

Hence, K = 3

Note: if a body remains x% submerged in a liquid of density y, then the density of the body is (x% of y) OR(another method)

Total weight of body will be equal to weight of water surrounded by body(bouyant force),which gives us density of body. Such as

If d and v are density and volume of body and w and O is density of water and oil.

So Wight of body = weight of water displaced by body.

d*v*g=w*0.6*v*g

So. d=600 kg/m3.

Now in the case of oil. same concept is applied.

Wight of body = Wight of oil displaced by body

d*v*g=O*0.4*v*g

So. O = 1500 kg/m3.

Now we know that. Relative density =K/2.

Relative density = oil density/water density

So . K/2 = 1500/1000

So K=3.