Q115 / 150 · MHT CET 2026 (15 April Shift 1) · Physics
The excess pressure inside the first soap bubble of radius $R_1$ is three times that inside the second soap bubble of radius $R_2$. The ratio of volumes of the first bubble to second bubble is
- A$1:3$
- B$1:6$
- Correct answerC$1:27$
- D$1:9$
Solution
The excess pressure inside a soap bubble of radius $R$ is given by $\Delta P = \dfrac{4T}{R}$.
Given that $\Delta P_1 = 3\Delta P_2$.
$\dfrac{4T}{R_1} = 3 \left(\dfrac{4T}{R_2}\right)$
$\dfrac{R_1}{R_2} = \dfrac{1}{3}$
The volume of a spherical bubble is $V = \dfrac{4}{3}\pi R^3$.
The ratio of their volumes is $\dfrac{V_1}{V_2} = \left(\dfrac{R_1}{R_2}\right)^3 = \left(\dfrac{1}{3}\right)^3 = \dfrac{1}{27}$.
Thus, the ratio of volumes is $1:27$.
Answer: $1:27$
Given that $\Delta P_1 = 3\Delta P_2$.
$\dfrac{4T}{R_1} = 3 \left(\dfrac{4T}{R_2}\right)$
$\dfrac{R_1}{R_2} = \dfrac{1}{3}$
The volume of a spherical bubble is $V = \dfrac{4}{3}\pi R^3$.
The ratio of their volumes is $\dfrac{V_1}{V_2} = \left(\dfrac{R_1}{R_2}\right)^3 = \left(\dfrac{1}{3}\right)^3 = \dfrac{1}{27}$.
Thus, the ratio of volumes is $1:27$.
Answer: $1:27$
Hence, the correct answer is option: 'C'.