Question-27 Water rises up to height ‘x’ in a capillary tube immersed vertically in water. When the whole arrangement is taken to a depth ‘d’ in a mine, the water level rises up to height Y. If R is the radius of the earth then the ratio Y:x is
(A) R:(R+d)
(B) R:(R-d)
(C) R:(R-d)^2
(D) R:(R+d)^2
Answer : (B)
Explanation:
Rise in capillary tube is given as, h = \frac{2T \cos \theta}{r \rho g}
As all the other quantities are kept constant, in mine of depth d, h ∝ \frac{1}{g}
At a depth d, g_d = g\left(\frac{1 - d}{R}\right)
Also, given that, h = x and h_d = Y
∴ \frac{x}{Y} = \frac{g_d}{g} = \left(\frac{1 - d}{R}\right)
⇒ \frac{Y}{x} = \frac{R}{R - d}