Answer:
Option C
Explanation:
Key Idea The force per unit area is pressure. The pressure inside a soap bubble of radius R, is given by
$P=\frac{4T}{R}$
where T= surface tension
and R= radius of the drop
the pressure inside a soap bubble, $P=\frac{4T}{R}$
If a bubble is broken into 27 small soap bubbles then the volume of single bubble of radius R and the combined volume of 27 bubbles of radius r would be constant.
27 x volume of small bubbles = volume of larger bubble
$\Rightarrow$ $ 27\left(\frac{4}{3}\pi r^{3}\right)=\frac{4}{3}\pi R^{3}$
$\Rightarrow $ $27 r^{3}= R^{3}$
$\Rightarrow $ $r=\frac{R}{3}$ .............(i)
Now, the pressure inside smaller soap bubble,
$P_{small}=\frac{4T}{r}=\frac{12 T}{R}$ (using the relation)
and similarly $P_{large}=\frac{4t}{R}$
$\therefore$ Ratio of pressure of the smaller and larger soap bubble is given as,
$\frac{P_{larger}}{P_{small}}=\frac{4T}{R}\times\frac{R}{12T}=\frac{1}{3}$
$P_{larger}:{P_{small}}=1:3$
Hence, the ratio of mechanical force acting per unit area of big soap bubble to that of a small bubble is 1:3
