A glass capillary sealed at the upper end is of length $0.11 m$ and internal diameter $2 \times 10^{- 5} m$ . The tube is immersed vertically into a liquid of surface tension $5.06 \times 10^{- 2} N / m$ . To what length has the capillary to be immersed so that the liquid levels inside and outside the capillary become the same? What will happen to the water levels inside the capillary if the seal is now broken?

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$5 cm$

$2 cm$

$3 cm$

$1 cm$

answer is B.

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Detailed Solution

$p - \frac{2 T}{R} = p_{0} P = \frac{2 T}{R} + P_{0} R = \frac{r}{cosθ} For water θ = 0 ° ∴ R = r P = \frac{2 T}{r} + P_{0} or As temperature is constant, p_{1} V_{1} = p_{2} V_{2} ∴ p_{0} (0.11) = p (0.11 - h) or p_{0} (0.11) = (p_{0} + \frac{2 T}{r}) (0.11 - h) Substituting the values, we get (1.01 \times 10^{5} (0.11) = [1.01 \times 10^{5} + \frac{2 \times 5.06 \times 10^{- 2}}{10^{- 5}}] (0.11 = h) Solving this equation we get, h = 0.01 m or 1 cm$