If work W is done in blowing a bubble of radius R from a soap solution, then the work done in blowing a bubble of radius 2R from the same solution is

The correct option is 4W.

Step-by-step Explanation:
When a soap bubble is blown in air, it has two free surfaces (an inner surface and an outer surface) in contact with the air.
The work done $W$ in blowing a soap bubble of radius $R$ is equal to the increase in its surface energy.
The formula for the work done in blowing a soap bubble of radius $R$ with surface tension $T$ is given by:

$W=2\times T\times A$

where $A$ is the surface area of a sphere of radius $R$, which is $4\pi R^2$.
Substituting the area into the equation:

$W=2\times T\times \left(4\pi R^2\right)=8\pi T{R}^2$

From this expression, we can see that since the surface tension $T$ of the same soap solution remains constant, the work done $W$ is directly proportional to the square of the radius $R$ of the bubble:

$W\propto R^2$

Let $W_1=W$ be the work done for a bubble of radius $R_1=R$.
Let $W_2$ be the work done for blowing a bubble of radius $R_2=2R$.
Taking the ratio of the work done in both cases:

$\frac{W_2}{W_1}={\left(\frac{R_2}{R_1}\right)}^2$

Substituting the given values:

$\frac{W_2}{W}={\left(\frac{2R}{R}\right)}^2$

$\frac{W_2}{W}=2^2=4$

$W_2=4W$

Therefore, the work done in blowing a bubble of radius 2R from the same solution is 4W.