A capillary tube of radius $0.1\ \text{mm}$ is partly dipped in water (surface tension $70\ \text{dyn/cm}$ and glass–water contact angle $\approx 0^\circ$), inclined at $30^\circ$ with the vertical. The length of water risen in the capillary is ______ cm. (Take $g = 9.8\ \text{m/s}^2$)
Answer: (A) $\dfrac{82}{5}$
The vertical height of the column does not depend on the tilt (CGS units, $r = 0.01\ \text{cm}$):
$$h = \frac{2T\cos\theta}{\rho gr} = \frac{2\times70\times1}{1\times980\times0.01} = \frac{100}{7}\ \text{cm} \approx 14.3\ \text{cm}$$
Along a tube tilted $30^\circ$ from the vertical, the length of the column is
$$l = \frac{h}{\cos30^\circ} = \frac{100}{7}\times\frac{2}{\sqrt3} \approx 16.5\ \text{cm}$$
The closest option is $\dfrac{82}{5} = 16.4\ \text{cm}$.
Solution by Sreeraj P, M.Sc Physics