The ratio of surface tensions of mercury and | vedclass

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(D) The height of capillary rise or depression is given by the formula $h = \frac{2S \cos 	heta}{r ho g}$.For mercury $(1)$: $h = \frac{2S_1 \cos \

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$2/5$

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(D) The height of capillary rise or depression is given by the formula $h = \frac{2S \cos 	heta}{r ho g}$.For mercury $(1)$: $h = \frac{2S_1 \cos 	heta_1}{r_1 ho_1 g}$.For water $(2)$: $h = \frac{2S_2 \cos 	heta_2}{r_2 ho_2 g}$.Since the magnitude of $h$ is the same,we equate them: $\frac{2S_1 \cos 	heta_1}{r_1 ho_1 g} = \frac{2S_2 \cos 	heta_2}{r_2 ho_2 g}$.Rearranging for the ratio $\frac{r_1}{r_2}$: $\frac{r_1}{r_2} = \frac{S_1}{S_2} \cdot \frac{ho_2}{ho_1} \cdot \frac{\cos 	heta_1}{\cos 	heta_2}$.Given: $\frac{S_1}{S_2} = 7.5$,$\frac{ho_1}{ho_2} = 13.6 \Rightarrow \frac{ho_2}{ho_1} = \frac{1}{13.6}$,$	heta_1 = 135^o$,$	heta_2 = 0^o$.$\cos 135^o = -\frac{1}{\sqrt{2}}$ and $\cos 0^o = 1$.Taking the magnitude of the depression/rise: $\frac{r_1}{r_2} = 7.5 	imes \frac{1}{13.6} 	imes \frac{1/\sqrt{2}}{1} \approx 7.5 	imes 0.0735 	imes 0.707 \approx 0.39$. This is approximately equal to $2/5 = 0.4$.

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