Question

The lower end of a capillary tube is immersed in mercury. The level of mercury in the tube is found to be 2 cm below the outer level. If the same tube is immersed in water, up to what height will the water rise in the capillary?

Answer 1

5.9cm

Explanation:

Given statement

The level of mercury in the tube, $h_1= 2cm$

Formula, $h_1 = \frac {2T_1\cos\theta_1}{r\rho_1 g}$........ 1

$\rho_1$ is density of mercury.

The level of water in the tube, $h_2 = \frac {2T_2\cos\theta_2}{r\rho_2 g}$-----2

$\rho_2$ is density of water.

radius of the capillary will remain same = r

$\theta_1 = 135^o$ in eq. 1

$2 = \frac {2(484.5)\cos135^o}{r(13.6)(980)}$

$r = \frac{685.083}{26656}$

$r = 0.025cm$

Put value of r and $\theta = 0^o$ in eq. 2

$h_2 = \frac{2(72.7)\cos0^o}{(0.025)(1)(980)}$

$h_2 = 5.9cm$