The maximum diameter that a capillary tube can have to ensure that a capillary rise of at least 6 mm is achieved when the tube is dipped into a body of liquid with surface tension =0.08N/m and density =900kg/m³, is-

Correct option is B

​$$\text{To solve this problem, we use the formula for capillary rise:} \\h = \frac{4\sigma \cos\theta}{\rho g d} \\[6pt]\text{Where:} \\h = \text{capillary rise} = 6\,\text{mm} = 0.006\,\text{m} \\\sigma = 0.08\,\text{N/m} \ (\text{surface tension}) \\\rho = 900\,\text{kg/m}^3 \ (\text{density of the liquid}) \\g = 9.81\,\text{m/s}^2 \ (\text{acceleration due to gravity}) \\\theta = 0^\circ \Rightarrow \cos\theta = 1 \\d = \text{Diameter of the capillary tube} \\[6pt]\text{Rearranging the formula to find } d: \\d = \frac{4\sigma \cos\theta}{\rho g h} \\[6pt]d = \frac{4 \times 0.08 \times 1}{900 \times 9.81 \times 0.006} \\[4pt]d = 6.04\,\text{mm}$$​​