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_1)/(d_2) V`
B. `((d_(1)-d_(2))/(d_1))V`
C. `((d+d_(2))/(d_(1)+d_(2)))V`
D. `((d-d_(2))/(d_(1)-d_(2)))V`

Answer

D

Explanation

`V d g = V_(1)d_(1)g + V_(2) d_(2)g`…(i) also `V = V_(1) +V_(2)`
or, `Vd_(2)g = V_(1)d_(2)g + V_(2)d_(2)g` …(ii)
(i) - (ii) gives
`V_(g)(d-d_(2)) = V_(g)(d-d_(2)) = V_(1)g(d_(1)-d_(2)) or V_(1) = (d-d_(2))/(d_(1)-d_(2)) V`.