The fraction of a floating object of volume `V_(0)` and density `d_(0)` above the surface of a liquid of density d will be

Options

A. `(d_0)/(d)`
B. `(dd_(0))/(d+d_(0))`
C. `(d-d_(0))/(d)`
D. `(dd_(0))/(d-d_(0))`

Answer

C

Explanation

Let `v` be the volume of the object above the surface of the liquid. If `V` be the total volume of the object, then
`(V-v)dg = V d_(0)g`
`or `(V_v)/(V) = (d_0)/(d) or (v)/(V) = 1 -(d_0)/(d) = (d-d_(0))/(d)`.