The height of liquid column raised in a capillary tube of certain radius when dipped in liquid $$A$$ vertically is, $$5$$ cm. If the tube is dipped in a similar manner in another liquid $$B$$ of surface tension and density double the values of liquid $$A$$, the height of liquid column raised in liquid B would be ______ m.

We need to find the capillary rise in liquid B, given that the rise in liquid A is 5 cm.

$$h = \frac{2T\cos\theta}{\rho g r}$$

For liquid B: $$T_B = 2T_A$$ and $$\rho_B = 2\rho_A$$

Assuming same contact angle and same capillary tube.

$$\frac{h_B}{h_A} = \frac{T_B}{T_A} \times \frac{\rho_A}{\rho_B} = \frac{2T_A}{T_A} \times \frac{\rho_A}{2\rho_A} = 2 \times \frac{1}{2} = 1$$

$$h_B = h_A = 5$$ cm $$= 0.05$$ m

The height of liquid column raised in liquid B is $$0.05$$ m.

The correct answer is Option 3: $$0.05$$ m.