Question

Water rises to a height of 10cm in a capillary tube and mercury falls to a depth of 3.42 cm in the same capillary tube. If the density of mercury is 13.6g/cc and the angle of contact of mercury and water are ${135}^o$ and $0^o$ respectively, the ratio of surface tension of water and mercury is

• A. 1 : 0.15
• B. 1 : 3
• C. 1 : 6.5
• D. 1.5 : 1

Answer 1

The correct option is

B

1 : 6.5

$h=\frac{2Scos\theta }{r\rho g}$
$ors=\frac{hr\rho g}{2cos\theta }$
$ors\alpha \frac{h\rho }{cos\theta }$
$\frac{S_w}{S_{Hg}}=\frac{h_1}{h_2}\times \frac{cos{\theta }_2}{cos{\theta }_1}\times \frac{{\rho }_1}{{\rho }_2}$
Putting the values, we obtain 1:6.5
Hence, (B) is correct.