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Properties of Matter question

2020 · 3 Sep · Shift 1 · Q59

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JEE Main
Physics
Properties of Matter
2020 · 3 Sep · Shift 1 · Q59

Properties of Matter question

2020 · 3 Sep · Shift 1 · Q59

JEE MainPhysicsProperties of MatterMCQ+4 / −1

Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is :

A
4 : 1
B
8 : 1
C
2 : 1
D
0.8 : 1

View written solutionFree

Correct answer: B

Use excess pressure formula for a soap bubble

For a soap bubble, the excess pressure inside is

\Delta P = \frac{4T}{r}

where $T$ is surface tension and $r$ is radius.

So the internal pressure is

P_{\text{in}} = P_{\text{atm}} + \frac{4T}{r}

Write for the two bubbles

Given:

P_1 = 1.01\,\text{atm}, \qquad P_2 = 1.02\,\text{atm}

Assuming atmospheric pressure outside is

P_{\text{atm}} = 1\,\text{atm}

So the excess pressures are

\Delta P_1 = 1.01 - 1 = 0.01\,\text{atm}

\Delta P_2 = 1.02 - 1 = 0.02\,\text{atm}

Relate radius to excess pressure

Since

\Delta P \propto \frac{1}{r}

we get

r \propto \frac{1}{\Delta P}

Hence,

\frac{r_1}{r_2} = \frac{\Delta P_2}{\Delta P_1} = \frac{0.02}{0.01} = 2

Find ratio of volumes

Volume of a sphere:

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

Therefore,

\frac{V_1}{V_2} = \left(\frac{r_1}{r_2}\right)^3 = 2^3 = 8

So,

V_1 : V_2 = 8 : 1

Check options

A: $4:1$ ❌
B: $8:1$ ✅
C: $2:1$ ❌
D: $0.8:1$ ❌

Therefore, the correct answer is B.

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