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Physics · Mechanical Properties of Matter

JEE Main 2024 — 9 April, Shift 2 — Question 38

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is :

  1. Option A:

    1:91: 9

  2. Option B:

    1:31: 3

  3. Option C:

    1:811: 81

  4. Option D:

    1:271: 27

    Correct

Answer: D

Step-by-step solution

P1−P0=4 Tr1\mathrm{P}_{1}-\mathrm{P}_{0}=\frac{4 \mathrm{~T}}{\mathrm{r}_{1}}

P1−P0=3(P2−P0)\mathrm{P}_{1}-\mathrm{P}_{0}=3\left(\mathrm{P}_{2}-\mathrm{P}_{0}\right)

4 Tr1=34 Tr2\frac{4 \mathrm{~T}}{\mathrm{r}_{1}}=3 \frac{4 \mathrm{~T}}{\mathrm{r}_{2}}

r2=3r1\mathrm{r}_{2}=3 \mathrm{r}_{1}

V1 V2=43πr1343πr23=127\frac{\mathrm{V}_{1}}{\mathrm{~V}_{2}}=\frac{\frac{4}{3} \pi \mathrm{r}_{1}^{3}}{\frac{4}{3} \pi \mathrm{r}_{2}^{3}}=\frac{1}{27}

P2−P0=4 Tr2\mathrm{P}_{2}-\mathrm{P}_{0}=\frac{4 \mathrm{~T}}{\mathrm{r}_{2}}

Solution figure

Answer key and solution verified before publishing.

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Exam
JEE Main 2024
Paper
9 April, Shift 2
Subject
Physics
Chapter
Mechanical Properties of Matter
Topic
Surface Tension and Surface Energy

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