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

For the floatation `V_(0)d_(0)g = V_(in)dg`
`implies V_(in) = V_(0)(d_0)/(d)`
`:. V_(out) = V_(0)-V_(in) = V_(0)-V_(0)(d_0)/(d) = V_(0)[(d-d_(0))/(d)]`
`implies (V_(out))/(V_0) = (d-d_(0))/(d)`.