JEE PYQ: Mechanical Properties Of Fluids Question 11
Question 11 - 2020 (03 Sep 2020 Shift 1)
Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is:
(1) 4:1
(2) 0.8:1
(3) 8:1
(4) 2:1
Show Answer
Answer: (3) 8:1
Solution
According to question, pressure inside 1st soap bubble: $\Delta P_1 = P_1 - P_0 = 0.01 = \frac{4T}{R_1}$ …(i) And $\Delta P_2 = P_2 - P_0 = 0.02 = \frac{4T}{R_2}$ …(ii) Dividing equation (ii) by (i): $\frac{1}{2} = \frac{R_2}{R_1} \Rightarrow R_1 = 2R_2$ Volume $V = \frac{4}{3}\pi R^3$ $\therefore \frac{V_1}{V_2} = \frac{R_1^3}{R_2^3} = \frac{8R_2^3}{R_2^3} = \frac{8}{1}$
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