JEE PYQ: Mechanical Properties Of Fluids Question 10
Question 10 - 2020 (02 Sep 2020 Shift 2)
A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide (surface tension = 0.05 Nm$^{-1}$, density = 667 kg m$^{-3}$) which rises to height $h$ in the tube. It is observed that the two tangents drawn from liquid-glass interfaces (from opp. sides of the capillary) make an angle of 60$^\circ$ with one another. Then $h$ is close to ($g = 10$ ms$^{-2}$):
(1) 0.049 m
(2) 0.087 m
(3) 0.137 m
(4) 0.172 m
Show Answer
Answer: (2) 0.087 m
Solution
Given, angle of contact $\theta = 30^\circ$ Surface tension, $T = 0.05$ Nm$^{-1}$ Radius of capillary tube, $r = 0.15$ mm $= 0.15 \times 10^{-3}$ m Density of methylene iodide, $\rho = 667$ kg m$^{-3}$
Capillary rise, $h = \frac{2T\cos\theta}{\rho g r} = \frac{2 \times 0.05 \times \frac{\sqrt{3}}{2}}{667 \times 10 \times 0.15 \times 10^{-3}} = 0.087$ m
BETA
