Q110 / 150 · MHT CET 2023 (09 May Shift 2) · Physics

A soap bubble of radius ' $R$ ' is blown. After heating a solution, a second bubble of radius ' $2 \mathrm{R}$ ' is blown. The work required to blow the $2^{\text {nd }}$ bubble in comparison to that required for the $1^{\text {st }}$ bubble is

  • A
    exactly double.
  • B
    slightly more than 4 times.
  • Correct answer
    C
    slightly less than 4 times.
  • D
    slightly less than double.

Solution

$\begin{aligned} \mathrm{W}_1 & =8 \pi \mathrm{R}^2 \mathrm{~T}_1 \\ \mathrm{~W}_2 & =8 \pi(2 \mathrm{R})^2 \mathrm{~T}_2=32 \pi \mathrm{R}^2 \mathrm{~T}_2 \\ \therefore \quad \frac{\mathrm{W}_1}{\mathrm{~W}_2} & =\frac{\mathrm{T}_1}{4 \mathrm{~T}_2} \end{aligned}$ When $\mathrm{T}_1=\mathrm{T}_2, \mathrm{~W}_2=4 \mathrm{~W}_1$ But as work is done, temperature increases and surface tension decreases. $\therefore \quad \mathrm{W}_2 < 4 \mathrm{~W}_1$

Hence, the correct answer is option: 'C'.

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