A stream line body with relative density `rho_(1)` falls into air from a height `h_(1)` on the surface of a liquid of realtive density `rho_(2)`, where `rho_(2) gt rho_(1)`. Find the time of immersion of the body into the liquid.

Explanation

velocity of body when it touches the surface of liquid is `upsilon_(1) = sqrt(2 gh_(1))`
Buoyant force on the body, `F_(B)=V rho_(2)g`
Retardation in the body.
`a=(Vrho_(2)g-V rho_(1)g)/(m)`
`(Vrho_(2)g-V rho_(1)g)/(V rho_(1)) = ((rho_(2)-rho_(1))g)/(rho_1)`
Using the relation , `upsilon = u+at,` we have
`upsilon = 0, u= upsilon_(1), a=-a , t=?`
then `t=(upsilon_(1))/(a) = (sqrt(2gh_(1)))/((rho_(2)-rho_(1))g) xx rho_(1)`
`= (rho_1)/(rho_(2)-rho_(1)) (sqrt((2h_(1))/(g)))`.