At $ 0{}^\circ C $ , the densities of a cork and a liquid, in which the cork floats are $ {{S}_{1}} $ and $ {{S}_{2}} $ respectively. The coefficients of expansion of the material of the cork and the liquid are 100r and respectively. If the cork sinks when temperature of the liquid is t $ {}^\circ C $ , then the $ \left( \frac{{{P}_{2}}}{{{P}_{1}}} \right) $ is: