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 vertical. The length of water risen in the capillary is _____ cm. (Take g = 9.8 ) [2025]

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Solution

Q.
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 vertical. The length of water risen in the capillary is _____ cm. (Take g = 9.8 $m / s^{2}$ ) [2025]

1 $\frac{82}{5}$

2 $\frac{57}{2}$

3 $\frac{71}{5}$

4 $\frac{68}{5}$

Ans.
(1)

$h = \frac{2 T \cos θ}{ρ g r} = \frac{2 \times 70 \times 1}{1 \times 980 \times 10^{- 2}} = \frac{100}{7} cm$

$\sin 60 ° = \frac{h}{l} \Rightarrow l = \frac{h \times 2}{\sqrt{3}}$

$l = \frac{100}{7} \times \frac{2}{\sqrt{3}} = \frac{200}{7 \times \sqrt{3}} = 16.49 cm$

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