When a long glass capillary tube of radius 0.015 cm is dipped in a liquid, the liquid rises to a height of 15 cm within it. If the contact angle between the liquid and glass to close to 0ᵒ, the surface tension of the liquid, in milliNewton m–1, is [ρ (liquid) = 900 kgm –3 , g = 10 ms –2 ]
(Give answer in closest integer) _____.

Solution

Physics sir · 4 steps

Jurin's law links the rise to surface tension; convert r and h to metres first, then solve for T.

1. Capillary rise formula. The upward pull of surface tension around the rim balances the weight of the raised liquid column. With contact angle θ ≈ 0°, cos θ = 1.

   h = (2T cos θ)/(rρ g) ⇒ T = (h r ρ g)/2

2. SI units. r = 0.015 cm = 1.5 × 10⁻⁴ m and h = 15 cm = 0.15 m.
3. Put in numbers. T = (0.15 × 1.5 × 10⁻⁴ × 900 × 10)/2 = 0.2025/2 = 0.10125 N m⁻¹.
4. So. T = 101.25 mN m⁻¹, which rounds to 101.

The common slip: 203. Dropping the factor 2 in Jurin's law gives 202.5 mN m⁻¹, about 203, not 101.

The idea to keep. For capillary rise, h = (2T cos θ)/(rρ g). The 2 is there because the contact line is a circle of circumference 2π r. Put every length in metres before you substitute.

Answer from the NTA final answer key. Solution by PrepWiser.