JEE PYQ: Mechanical Properties Of Fluids Question 25
Question 25 - 2019 (10 Apr 2019 Shift 1)
The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of their densities is 13.6. Their contact angles, with glass, are close to 135$^\circ$ and 0$^\circ$, respectively. It is observed that mercury gets depressed by an amount $h$ in a capillary tube of radius $r_1$, while water rises by the same amount $h$ in a capillary tube of radius $r_2$. The ratio, ($r_1/r_2$), is then close to:
(1) 4/5
(2) 2/5
(3) 3/5
(4) 2/3
Show Answer
Answer: (2) 2/5
Solution
As we know that $h = \frac{2T\cos\theta}{r\rho g}$ $\frac{T_{Hg}}{T_{Water}} = 7.5$ $\frac{\rho_{Hg}}{\rho_W} = 13.6$, $\frac{\cos\theta_{Hg}}{\cos\theta_W} = \frac{\cos 135^\circ}{\cos 0^\circ} = \frac{-1}{\sqrt{2}}$ $\frac{r_1}{r_2} = \left(\frac{T_{Hg}}{T_W}\right) \left(\frac{\rho_W}{\rho_{Hg}}\right) \left(\frac{\cos\theta_{Hg}}{\cos\theta_W}\right)$ $= 7.5 \times \frac{1}{13.6} \times \frac{1}{\sqrt{2}} = 0.4 = \frac{2}{5}$
BETA
