A small body with relative density `d_(1)` falls in air from a height 'h' on to the surface of a liquid of relative density `d_(2)` where `d_(2)gt d_(1)`. The time elapsed after entering the liquid to the instant when it comes to instantaneous rest inside liquid

Options

A. `sqrt((2h)/(g))(d_(2))/(d_(1))`
B. `sqrt((2h)/(g))((d_(1))/(d_(2)-d_(1)))`
C. `sqrt((2h)/(g))(d_(1))/(d_(2))`
D. `sqrt((2h)/(g))((d_(2)-d_(1)))/(d_(1))`

Answer

D

Explanation

`(dQ)/(dt)=-KA (dT)/(dx)=-alphaTA (dT)/(dx)`
`(dQ)/(dt)=-alphaAT(dT)/(dx)impliesi=-alphaAT(dT)/(dx)implies iintdx =- alphaAunderset(T_(1))overset(T_(2))intTdT`
`implies i(l)=alphaA((T_(1)^(2)-T_(1)^(2)))/(2)implies i=(alphaA)/(2l)(T_(1)^(2)-T_(2)^(2))`