Question

If a $5\text{cm}$ long capillary tube with $0.2\text{mm}$ internal diameter open at both ends is slightly dipped in water having surface tension $75\text{dyne/cm}$. What will be the rise of water in capillary $($Take $g=1000\text{cm}/s^2$$)$

• A. $15\text{cm}$
• B. $5\text{cm}$
• C. $10\text{cm}$
• D. $20\text{cm}$

Answer 1

The correct option is B $5\text{cm}$

Given that
Surface tension, $T=75\text{dyne/cm}$
Radius, $\left(r\right)=\frac{0.2}{2}\text{mm}=0.1\text{m}=0.01\text{cm}$
Density of water, $\rho =1\text{gm}/c{m}^3$
Angle of contact, $\theta =0^o$
Let $h$ be the height to which water will rises in the capillary tube. Then
$h=\frac{2T\cos \theta }{r\rho g}=\frac{2\times 75\times \cos 0}{0.01\times 1\times 1000}=15\text{cm}$
But legth of capilalry tube is $5\text{cm}$
Because the tube is of insufficient length therefore the water will rise upto the upper end of the tube.
$h=5\text{cm}$

Why this question? Tips: If length of tube < height of capillary rise, then the total rise of water in capillary will be equal to the length of the tube but angle of contact will change.