Two soap bubbles have radii in the ratio of 2:1. What is the ratio of excess pressures inside them?

Question

Two soap bubbles have radii in the ratio of 2:1. What is the ratio of excess pressures inside them? (A) 1: 2 (B) 1: 4 (C) 2: 1 (D) 4: 1

Tardigrade Admin · Accepted Answer

Excess pressure inside the bubble, p=(4 T/r) Then, p1=(4 T/r1) ... (i) P2 =(4 T/r2) ...(ii) From Eqs. (i) and (ii), we have (p1/p2)=(4 T / r1/4 T / r2)=(r2/r1) (p1/p2)=(1/2)

Q. Two soap bubbles have radii in the ratio of $2 : 1$ . What is the ratio of excess pressures inside them?

1 : 2

1 : 4

2 : 1

4 : 1

Excess pressure inside the bubble,
$p = \frac{4 T}{r}$
Then, $p_{1} = \frac{4 T}{r _{1}}$ ... (i)
$P_{2} = \frac{4 T}{r _{2}}$ ...(ii)
From Eqs. (i) and (ii), we have
$\frac{p _{1}}{p _{2}} = \frac{4 T / r _{1}}{4 T / r _{2}} = \frac{r _{2}}{r _{1}}$
$\frac{p _{1}}{p _{2}} = \frac{1}{2}$

Q. Two soap bubbles have radii in the ratio of 2:1. What is the ratio of excess pressures inside them?