Question

Air is pushed into a soap bubble of radius R to triple its radius. If the surface tension of the soap solution
is S, the work done in the process is:
1) 72 S πR²
2) 64 S πR²
3) 36 S πR²
4) 32S πR²

Answer 1

Answer:

2nd option is your answer

Answer 2

Work done is 32S πR² (Option 4)

Given:

• Radius of soap bubble increases from R to 3R.
• Surface tension is S.

To find:

Work done ?

Calculation:

Initial surface energy will be :

$U1 = S \times 4\pi{R}^{2}$

Now, after increase of radius, new surface energy will be :

$U2= S \times 4\pi{(3R)}^{2}$

$\implies U2=(9 \times 4) S \times \pi{R}^{2}$

$\implies U2=36 S \times \pi{R}^{2}$

So, work done is :

$W = U2 - U1$

$\implies W =(36 - 4)S \times \pi{R}^{2}$

$\implies W =32S \pi{R}^{2}$

So, option 4) is correct.