A solid body is found floating in water with `((alpha)/(beta))^(th)` of its volume submerged. The same solid is found floating in a liquid with `((alpha)/(beta))^(th)`of its volume above the liquid surface. The specific gravity of the liquid is

Options

A. `(beta-alpha)/(alpha)`
B. `(alpha-beta)/(beta)`
C. `(alpha)/(beta-alpha)`
D. `(beta)/(alpha-beta)`

Answer

C

Explanation

`(alpha)/(beta)=(d_(b))/(d_(w))` ….(1)
`1-(alpha)/(beta)=(d_(b))/(d_(1))` …(2)
From 1 and 2 `(d_(l))/(d_(b))=(alpha)/(beta-alpha)`