Question

Work done in forming a soap bubble of radius R is W. Then workdone is forming a soap bubble of radius '2R' will be:

• A. 2W
• B. 4W
• C. W/2
• D. W/4

Answer 1

The correct option is B 4W

$\begin{array}{cc}\text{let, the surface tension}& =T\\ \text{Surface Area}& =A\end{array}$

Since, soap buble has two Surface are,

$\begin{array}{cc}\text{Surface Enengy}{E}_1=& 2\times T\times A\\ =& 2\times T\times 4\pi R^2\\ =& 8\pi R^{2}T\\ \therefore E_1=8\pi R^{2}T& \end{array}$

Surface Enengy of the bubble with

Radius $2R$ is , let $E_2$

$\begin{array}{cc}\therefore E_2& =2\times T\times (4\pi \cdot (2R{)}^2)\\ & =2\times T\times 16\pi R^2\\ & =32\pi R^{2}T\\ \therefore E_2& =32\pi R^{2}T\end{array}$

according to question

$\begin{array}{cc}\frac{E_2}{E_1}=\frac{32\pi R^{2}T}{8\pi R^{2}T}& \\ \text{or}\frac{E_2}{W}=4& \therefore E_1=W\end{array}$

$E_2=4W$

Correct option : $\left(B\right)$