Question

A glass rod of side $'r'$ is inserted into a vertical capillary tube of radius $'R'$ such that their lower ends are at the same level as shown in figure. The arrangement is now dipped in water. The height to which water will rise into the tube, will be ( $T=$ surface tension of water, $\rho =$ density of water and the contact angle between the glass and water is $0^\circ $ )

• A. $\frac{T \left(\pi R + 2 r\right)}{\left(\pi R^{2} - r^{2}\right) \rho g}$
• B. $\frac{2 T \left(\pi R + 2 r\right)}{\left(\pi R^{2} - r^{2}\right) \rho g}$
• C. $\frac{T \left(\pi R + 2 r\right)}{2 \left(\pi R^{2} - r^{2}\right) \rho g}$
• D. $\frac{2 T \left(\pi R + 2 r\right)}{3 \left(\pi R^{2} - r^{2}\right) \rho g}$

Answer 1

Answer: (B)

Total upward force due to surface tension $=$ weight of the liquid column of height $h$ .
$T\cdot 2\pi R+T\cdot 4r=\rho \left(\pi R^{2} - r^{2}\right)gh$
$h=\frac{2 T \left(\pi R + 2 r\right)}{\left(\pi R^{2} - r^{2}\right) \rho g}$