Q. An air bubble doubles its radius on raising from the bottom of water reservoir to be the surface of water in it. If the atmospheric pressure is equal to $10\ m$ of water, the height of water in the reservoir is
A) $10\ m$
B) $20\ m$
C) $70\ m$
D) $80\ m$
Explanation
(c) According to Boyle’s law $\left( P_{1}V_{1} \right)_{bottom} = \left( P_{2}V_{2} \right)_{top}$
$(10 + h) \times \frac{4}{3}\pi r_{1}^{3} = 10 \times \frac{4}{3}\pi r_{2}^{3}$ but $r_{2} = 2r_{1}$
$\therefore(10 + h)r_{1}^{3} = 10 \times 8r_{1}^{3} \Rightarrow 10 + h = 80\ \therefore h = 70m$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.