At $0^{0} C$ 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? y and 100 y respectively. If the cork sinks when the temperature of the liquid is $^{'} t^{0} C^{'}$ then the ratio $\frac{d_{2}}{d_{1}}$ is?

\frac{1 + 100 y t}{1 + y t}

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\frac{1 + y t}{1 + 100 y t}

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\frac{100 + y t}{1 + y t}

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\frac{1 + y t}{100 + y t}

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