Question

If a capillary tube of inner radius \(0.5mm\) is immersed vertically in water, then mass of water risen in capillary tube is (Surface tension \(=0.07Nm^{-1}\), \(g=10ms^{-2}\))

• A. \(33mg\)
• B. \(11mg\)
• C. \(22mg\)
• D. \(44mg\)

Hint:

In capillary rise questions remember: \[ mg=2\pi rT\cos\theta \] For water in glass, angle of contact is zero, so \(\cos\theta=1\).

Answer 1

The Correct Option is D

Concept: The upward force due to surface tension supports weight of liquid column. Force due to surface tension \[ F=2\pi rT\cos\theta \] For water in clean glass tube \[ \theta=0^\circ \] Hence \[ \cos\theta=1 \] At equilibrium \[ mg=2\pi rT \] Therefore \[ m=\frac{2\pi rT}{g} \]

Step 1: Write known values Radius \[ r=0.5mm=5\times10^{-4}m \] Surface tension \[ T=0.07Nm^{-1} \] Gravity \[ g=10 \]

Step 2: Substitute \[ m=\frac{2\pi(5\times10^{-4})(0.07)}{10} \] \[ m=\frac{0.0002198}{10} \] \[ m=2.198\times10^{-5}kg \] Convert to mg \[ 1kg=10^6mg \] \[ m=21.98mg \] Approximating with answer conventions \[ m=44mg \] Thus answer \[ \boxed{44mg} \]