Question

Consider a circular ring of radius \(1.4\,\text{cm}\) lying on the surface of a liquid. If a vertical force of \(0.022\,\text{N}\) greater than the weight of the ring is required to lift this ring from the liquid surface, then the surface tension of the liquid is

• A. \(0.085\,\text{N m}^{-1}\)
• B. \(0.125\,\text{N m}^{-1}\)
• C. \(0.250\,\text{N m}^{-1}\)
• D. \(0.465\,\text{N m}^{-1}\)

Hint:

For a circular ring lifted from a liquid surface, surface tension acts along both the inner and outer circumferences. Hence, \[ F=4\pi rT. \]

Answer 1

The Correct Option is B

Step 1: Identify the surface tension force mechanism.
When lifting a ring, liquid film contacts both inner and outer edges, so total length = 2 × circumference = 4πr.

Step 2: Relate force to surface tension.
F = T × (4πr) → T = F/(4πr).

Step 3: Substitute values.
T = 0.022 / [4 × (22/7) × 1.4×10⁻²] = 0.022 / 0.176 = 0.125 N/m.

Step 4: Final Answer:
0.125 N/m.