If the work done in blowing a soap bubble of volume V is W , then the work done in blowing a soap bubble of volume 2 V under the same conditions will be

Question

If the work done in blowing a soap bubble of volume V is W , then the work done in blowing a soap bubble of volume 2 V under the same conditions will be (A) W (B) 2W (C) √2W (D) 41 / 3 W

Tardigrade Admin · Accepted Answer

The work done will be against surface tension and we know that surface tension is related to work as

W = T \times Δ A

Since, the surface area of sphere is

4 π R^{2}

and there are two free surfaces, we have

W = T \times 8 π R^{2} \dots (i)

and volume of sphere

V = \frac{4}{3} π R^{3}

\Rightarrow R = \frac{3 V}{4 π}^{1/3} \dots (ii)

From Eqs. (i) and (ii), we get

W = T \times 8 π \times \frac{3 V ^{2/3}}{4 π}^{2}

\Rightarrow W \propto V^{2/3}

∴ W_{1} \propto V_{1}^{2/3}

and,

W_{2} \propto V_{2}^{2/3}

\frac{w _{2}}{w _{1}} = \frac{2 v _{1}}{v _{1}}^{2/3}

\Rightarrow W_{2} = 2^{2/3} W_{1} = 4^{1/3} W

Q. If the work done in blowing a soap bubble of volume $V$ is $W$ , then the work done in blowing a soap bubble of volume $2 V$ under the same conditions will be

$W$

$2 W$

$2 W$

$4^{1/3} W$

Q. If the work done in blowing a soap bubble of volume V is W , then the work done in blowing a soap bubble of volume 2V under the same conditions will be

W

2W

2​W

41/3W

Q. If the work done in blowing a soap bubble of volume $V$ is $W$ , then the work done in blowing a soap bubble of volume $2 V$ under the same conditions will be

$W$

$2 W$

$2 W$

$4^{1/3} W$