Question

A light metal disc of radius ' \(r\) ' floats on water surface and bends the surface downwards along the perimeter making an angle ' \(\theta\) ' with the vertical edge of the disc. If the weight of water displaced by the disc is ' W ', the weight of the metal disc is [ \(\text{T}\) = surface tension of water]

• A. \(\text{W} - 2\pi\text{rT} \cos \theta\)
• B. \(2\pi r \text{ T} + \text{W}\)
• C. \(2\pi\text{rT} \cos \theta + \text{W}\)
• D. \(2\pi\text{rT} \cos \theta - \text{W}\)

Hint:

Surface tension force: $F = 2\pi r T \cos\theta$

Answer 1

The Correct Option is C

Concept: Upward forces:
• Buoyant force = $W$
• Surface tension force = $2\pi r T \cos\theta$

Step 1: Total upward force balances weight. \[ \text{Weight} = W + 2\pi r T \cos\theta \]

Step 2: Conclusion.
Weight of disc = $W + 2\pi r T \cos\theta$ Final Answer: Option (C)