Question

Work done in increasing the size of a soap bubble from a radius of $3cm$ to $5cm$ is nearly (Surface tension of soap solution $=0.03$ $N{m}^{-1}$):

• A. $4\pi$ $mJ$
• B. $0.2\pi$ $mJ$
• C. $2\pi$ $mJ$
• D. $0.4\pi$ $mJ$

Answer 1

The correct option is D $0.4\pi$ $mJ$

$W=($surface energy ${)}_{fina1}-($ surface energy ${)}_{initia1}$
$W=T\times 4\pi \left[\right(5\times {10}^{-2}{)}^2-(3\times {10}^{-2}{)}^2]\times 2$
$=4\pi \times 0.03\times 16\times {10}^{-4}\times 2$
$=4\pi \times 0.48\times {10}^{-4}\times 2$
$=1.92\pi \times {10}^{-4}\times 2$
$=3.94\pi \times {10}^{-4}=0.394\pi mJ\approx 0.4\pi mJ$