At `0.^(0)C` the densities of a cork and a liquid in which the cork floats are `d_(1)` and `d_(2)` respectively. The coefficient of expansion for the material of the cork and the liquid are `gamma` and `100gamma` respectively. If the cork sinks when the temperature of the liquid is `'t^(0)C'` then the ratio `(d_(2))/(d_(1))` is

Options

A. `(1 + 100gammat)/(1 + gammat)`
B. `(1 + gammat)/(1 + 100gammat)`
C. `(100 + gammat)/(1 + gammat)`
D. `(1 + gammat)/(100 + gammat)`

Answer

A

Explanation

`d_(f) = d_(1)(1 + gammat), (d_(2))/(d_(1)) = (d_(2))/(d_(1)) = (d_(1)(1 + gamma_(2)Deltat))/(d_(1)(1 + gamma_(1)Deltat))`