Question

If the work done in blowing a soap bubble of volume ${}^{\prime }{V}^{\prime }$ is $W$, then the work done in blowing is soap bubble of volume ${}^{\prime }2V^{\prime }$ is

• A. $4W$
• B. $8W$
• C. $2^{1/3}W$
• D. $4^{1/3}W$

Answer 1

The correct option is D $4^{1/3}W$

$W=T△A,$

$△A=$ change in Area

T = surface Area

$V=\frac{4}{3}\pi r^3$

$Area=4\pi r^2$

$\Rightarrow A\alpha v^{2/3}$

$\Rightarrow △A=(△v{)}^{2/3}$

$\Rightarrow \frac{W_1}{W_2}=\frac{△A_1}{△A_2}={\left(\frac{△V_1}{△V_2}\right)}^{2/3}$

$\Rightarrow W_2=W_1.{\left(\frac{2V}{V}\right)}^{2/2}$

$\Rightarrow W_2.2^{2/3}=4^{1/3}.w$