Question

Water rises to a height of 10cm in a capillary tube and mercury falls to a depth of 3.5cm in the same capillary tube. If the density of mercury is 13.6 gm/cc and its angle of contact is 135${}^o$ and density of water is 1 gm/cc and its angle of contact is 0${}^o$, then the ratio of surface tensions of two liquids is: (cos 135${}^o=$- 0.7)

• A. $1:14$
• B. $5:34$
• C. $1:5$
• D. $5:27$

Answer 1

The correct option is B $5:34$

By formula of capillary rise
$h=\frac{2Tcos\theta }{\rho gr}$
Therefore, $\frac{10}{-3.5}=\frac{2T_{w}cos{0}^0}{1\times g\times r}\times \frac{13.6\times g\times r}{2T_{M}cos{135}^0}$
$⟹\frac{T_W}{T_M}=\frac{10\times 0.7}{13.6\times 3.5}$(cos 135 = -0.7)
Hence, $\frac{T_W}{T_M}=\frac{5}{34}$
Hence, ratio of surface tension is 5 : 34