Question

The work done in blowing a bubble of radius R is W. What is the work done in making a bubble of radius 2R? Given both the bubble are to be made with the same solution.
(A) $W/2$
(B) $2W$
(C) $4W$
(D) $2\dfrac{1}{3}W$

Answer 1

Hint: In order to solve this question, we should know that a soap bubble or air bubble is acted upon on its surface force called surface tension and here we will use the general formula of work done on increasing the area of the bubble in terms of area and surface tension using given conditions.

Complete answer:
Start with the formula of amount of work done in blowing a soup bubble.
We know that, Work done is equal to tension in surface energy and surface energy is tension multiply to change in area as follows:
$W = T \times \Delta A$
Where,
$W = workdone$
$T = Surface\,tension$
$\Delta A = Area$

Now, in given case of soup bubble, work done will be;
$W = 8\pi {R^2}T$

From above equation we can see that;
$W \propto {R^2}$

Now the radius got doubled,
$W \propto {\left( {2R} \right)^2}$
$W \propto 4{R^2}$

Therefore, the work done get four times.
So, $Workdone = 4W$

Hence the correct answer is Option(C).

Note: While solving such questions, always remember that the surface tension acts normally on the surface of the surface and its equal in all direction which makes the work done formula symmeterically about any point on the whole spherical surface, so never confuse with surface tension being radial force, its a normal force.