Q 11-12-023NEETJEE MainMedium
An air bubble released at the bottom of a lake has three times its original volume when it reaches the surface. Assuming the temperature is the same throughout, the depth of the lake is about (atmospheric pressure $= 10^5$ Pa, $g = 10$ m s$^{-2}$)
Answer: (A) $20$ m
Concept. Boyle's law, then $p_{\text{bottom}} = p_0 + \rho gh$.
Step 1. Pressure at the bottom. $p_{\text{bottom}}V = p_0(3V) \Rightarrow p_{\text{bottom}} = 3 \times 10^5$ Pa.
Step 2. Depth. $\rho gh = 2 \times 10^5 \Rightarrow h = \dfrac{2 \times 10^5}{10^4} = 20$ m.
Answer. $20$ m (Option A).
Solution by Sreeraj P, M.Sc Physics