A body of density `d` and volume `V` floats with volumes `V` of its total volume `V` immersed in a liquid of density `d` and the rest of the volume `V_(2)` immersed in another liquid of density `d_(2)(ltd_(1))`. The volume `V_(1)` immersed in liquid of density `d_(1)` is

Options

A. `((d-d_(2))/(d_(1)-d_(2)))V`
B. `((d+d_(2))/(d_(1)+d_(2)))V`
C. `((d_(1)-d_(2))/(d_1))V`
D. `(d_1)/(d_2) V`

Answer

A

Explanation

`Vdg = V_(1) d_(1)g + V_(2)d_(2)g` ..(i)
Also , `V = V_(1)+V_(2)` ..(ii)
(i) - (ii) gives
`Vg(d-d_(2)) = V_(1) (d_(1)-d_(2))`
Or , ` V_(1) = (d-d_(2))/(d_(1)-d_(2)) V`.