A rectangular bar of soap having density `800kg//m^(3)` floats in water of density `1000kg//m^(3)`. Oil of density `300kg//m^(3)` is slowly added, forming a layer that does not mix with water. When the top surface of the oil is at the same level as the top surface of the soap. What is the ratio of the oil layer thickness to the soap's thickness `x//L`?

Options

A. `3/7`
B. `2/7`
C. `3/10`
D. `3/8`

Answer

B

Explanation

Let `A` be area of soap bar.

`PA -P_(0)A = mg implies (P-P_(0))A = mg`
`implies [300gx+100g(L-x)A = AL 800g]`
`implies x/L = 2/7`.