Question

The limbs of a U-tube are vertical and have internal diameters $0.5 \,cm$ and $1 \,cm$ respectively. If the tube contains water, what will be the difference in the surface level in the limbs? (Surface tension of water $= 72$ dyne/cm)

• A. 0.2938 cm
• B. 0.8938 cm
• C. 0.6938 cm
• D. None of these

Answer 1

Answer: (A)

For wider limb, $h_{1} \frac{2 T}{r_{1} d g}$
For the narrow limb, $h_{2} \frac{2 T}{r_{2} d g}$
$h_{2}-h_{1} \frac{2 T}{d g}\left(\frac{1}{r_{2}}-\frac{1}{r_{1}}\right)=\frac{2 \times 72}{1 \times 980}\left(\frac{1}{0.25}-\frac{1}{0.5}\right) $
$=\frac{2 \times 72}{980} \times \frac{0.25}{0.25 \times 0.5}=0.2938 \,cm$