A capillary tube of radius 0.1 mm is partly dipped in water (surface… | JEE Main 2025 (7 Apr, Shift 2)

Q23JEE Main 2025 · 7 APR · SHIFT 2Medium

Angle of Contact & Capillarity

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass water contact angle ≈ 0°) with 30° inclined with the vertical. The length of water risen in the capillary is _______ cm. (Take $g = 9.8$ m/s ${}^{2}$ )

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Answer: (a)

Vertical rise $h = \frac{2T}{r\rho g} = \frac{2 \times 0.07}{10^{-4} \times 10^3 \times 9.8} = \frac{1}{7}\text{ m} \approx 14.29\text{ cm}$ .
Length along the tube inclined at $30^\circ$ to the vertical: $l = \frac{h}{\cos 30^\circ} = \frac{14.29}{0.866}$
$l \approx 16.5\text{ cm} \approx \frac{82}{5}\text{ cm}$
So the answer is (a) $\frac{82}{5}$ .

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