The work done in blowing a soap bubble of 10cm radius is (surface tension of the soap solution is 3/100 N/m)

The correct option is 75.36 x 10��⁴ J.

To find the work done in blowing a soap bubble, let us analyze the physical parameters involved:
1. A soap bubble has two free surfaces in contact with air (one inside and one outside). Therefore, the increase in surface area is twice the area of a single sphere.
2. The radius of the soap bubble is given as:
$r=10\text{cm}=0.1\text{m}$
3. The surface tension of the soap solution is:
$T=\frac{3}{100}\text{N/m}=0.03\text{N/m}$

The formula for the work done ($W$) in blowing a soap bubble is given by:
$W=T\times \Delta A$
where $\Delta A$ is the total increase in surface area. Since a bubble has two surfaces:
$\Delta A=2\times \left(4\pi r^2\right)=8\pi r^2$

Substituting the expression for $\Delta A$ into the work formula:
$W=T\times 8\pi r^2$

Now, we substitute the given values:
$W=0.03\times 8\times 3.14\times {\left(0.1\right)}^2$
$W=0.24\times 3.14\times 0.01$
$W=0.7536\times 0.01$
$W=0.007536\text{J}$

Expressing this value in scientific notation to match the options:
$W=75.36\times {10}^{-4}\text{J}$

Thus, the work done in blowing the soap bubble is 75.36 x 10⁻⁴ J.