Question

The inside diameters of the two arms of a U-tube are $1.00mm$ and $1.5mm$ respectively. Now if it is partially filled with water having surface tension of $0.078N/m$ and zero contract angle, there what will be the difference in the level of menisci between the two arms?

• A.
  $2.1m$
• B.
  $3.8mm$
• C.
  $4.4mm$
• D.
  $10.6mm$

Answer 1

The correct option is D

$10.6mm$
Diameters of the two arms of the U-tube are $1.0mmand1.5mm$

Capillary rise in a tube, $h=\frac{2\sigma cos{\theta }_c}{\rho gr}$

For water contact angle ${\theta }_c=0\text{and specific weight,}{\rho }_g=9810N/m^3$

$\therefore h_1=\frac{2\times 0.078\times Cos{0}^{\circ }}{9810\times 0.5\times {10}^{-3}}=\frac{156}{4905}=0.0318m=31.8mm$

Also, $h_2=\frac{2\times 0.078cos{0}^{\circ }}{9810\times 0.75\times {10}^{-3}}=0.0212m=21.2mm$

$\therefore$ The difference in the level of menisci between the two arms is $31.8-21.2=10.6mm$