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WBJEE · Physics · Mechanical Properties of Fluids

Under isothermal conditions, two soap bubbles of radii a and b coalesce to form a single bubble of radius c. If the external pressure is \(\mathrm{P}\), then surface tension of the bubbles is

  1. A \(\frac{\mathrm{P}\left(\mathrm{c}^{3}-\mathrm{a}^{3}+\mathrm{b}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}\)
  2. B \(\frac{\mathrm{P}\left(\mathrm{c}^{3}-\mathrm{a}^{3}-\mathrm{b}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}\)
  3. C \(\frac{\mathrm{P}\left(\mathrm{c}^{2}+\mathrm{a}^{2}-\mathrm{b}^{2}\right)}{4\left(\mathrm{a}^{3}+\mathrm{b}^{3}-\mathrm{c}^{3}\right)}\)
  4. D \(\frac{\mathrm{P}\left(\mathrm{c}^{3}+\mathrm{b}^{3}-\mathrm{c}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{\mathrm{P}\left(\mathrm{c}^{3}-\mathrm{a}^{3}-\mathrm{b}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}\)

Step-by-step Solution

Detailed explanation

Total number of moles \(=\) constant…