Question

A capillary tube is taken from the earth to the surface of the moon. The rise of the liquid column on the moon (acceleration due to gravity on the earth is 6 times that of the moon)is

• A. six times that on the earths surface
• B. $ \frac{1}{6} $ that on the earths surface
• C. equal to that on the earths surface
• D. zero

Answer 1

Answer: (A)

From the relation $ h=\frac{2T\cos \theta }{rdg} $ where r = radius of capillary. h = rise or fall of the liquid. g = acceleration due to gravity. d = density of the liquid. $ \therefore $ $ h\propto \frac{1}{g} $ $ \Rightarrow $ $ \frac{{{h}_{2}}}{{{h}_{1}}}=\frac{{{g}_{1}}}{{{g}_{2}}} $ According to the question, On earth, $ {{h}_{1}}=h,\,{{g}_{1}}=g $ On moon, $ {{h}_{2}}=?\,{{g}_{2}}=\frac{g}{6} $ $ \frac{{{h}_{2}}}{h}=\frac{g}{g/6} $ $ \Rightarrow $ $ {{h}_{2}}=6h $ Hence, the rise of the liquid column on the moon becomes six time that on the earths surface.