A body of mass 6 kg is floating in a liquid with `(2)/(3)` of its volume inside the liquid. Find
(i) buoyant force acting on the body and
(ii) ratio between the density of the body and density of liquid. [Take `g=10m//s^(2)`].

Explanation

When a body floats, the buoyant force on the body is equal and opposite to the weight of body. So,
(i) Buoyant force = Weight of the body
`=6kgxx10m//s^(2)=60N`
(ii) Let V be the volume of the body.
Buoyant force = Weight of liquid displaced
`((2)/(3)V)rho_(1)g`
Weight of body `=Vrho_(b)g`
when body is floating, then
`Vrho_(b)g=(2)/(3)Vrho_(1)g`
(or) `(rho_b)/(rho_1)=(2)/(3)`