Two soap bubbles of radii \(\mathrm{x}\) and \(\mathrm{y}\) coalesee to constitute a bubble of radius \(\mathrm{z}\). Then \(\mathrm{z}\) is requal to

• Correct answer
  A

  \(\sqrt{x^2+y^2}\)
• B

  \(\sqrt{x+y}\)
• C

  \(x+y\)
• D

  \(\frac{x+y}{2}\)

Solution

Hints: \(\mathrm{n}=\mathrm{n}_1+\mathrm{n}_2\) \(\mathrm{pv}=\mathrm{p}_1 \mathrm{v}_1+\mathrm{p}_2 \mathrm{v}_2\)
\(\mathrm{p}_1=\mathrm{p}_0+\frac{4 \mathrm{~T}}{\mathrm{x}}, \mathrm{p}_2=\mathrm{p}_0+\frac{4 \mathrm{~T}}{\mathrm{y}}, \mathrm{p}=\mathrm{p}_0+\frac{4 \mathrm{~T}}{\mathrm{z}}\) If the process takes place is vaccume then \(\mathrm{p}_0=0\) \(\mathrm{p}_1=\frac{4 \mathrm{~T}}{\mathrm{x}}, \mathrm{p}_2=\frac{4 \mathrm{~T}}{\mathrm{y}}, \mathrm{p}=\frac{4 \mathrm{~T}}{\mathrm{z}}\) If process is isothermal \(\begin{aligned} & \therefore \mathrm{p}_1 \mathrm{v}_1+\mathrm{p}_2 \mathrm{v}_2=\mathrm{pv} \\ & \therefore \mathrm{z}=\sqrt{\mathrm{x}^2+\mathrm{y}^2} \end{aligned}\)

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