MHTCET 26 Apr 2025 Shift 1 Paper

Concept:Capillary rise is inversely proportional to the acceleration due to gravity, which decreases as we go deeper inside the Earth.Explanation:According to Jurin's law, the height of a liquid column in a capillary tube is:$$h = \frac{2T\cos\theta}{r\rho g}$$Here, $T$ is surface tension, $\theta$ is the contact angle, $r$ is the tube radius, $\rho$ is the density, and $g$ is the acceleration due to gravity.For the same tube and liquid, all factors except $g$ remain constant.Therefore, $h \propto \frac{1}{g}$.At the Earth's surface, the acceleration due to gravity is $g_1 = g$.At depth $d$ inside a mine, the acceleration due to gravity becomes:$$g_2 = g\left(1 - \frac{d}{R}\right)$$Now, taking the ratio of the heights:$$\frac{h_1}{h_2} = \frac{g_2}{g_1} = 1 - \frac{d}{R} = \frac{R-d}{R}$$Taking the reciprocal to obtain the required ratio:$$\frac{h_2}{h_1} = \frac{R}{R-d}$$This matches option D.Answer:$$\frac{h_2}{h_1} = \frac{R}{R-d}$$Hence, option D is correct.