Question

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

Answer 1

The correct option is C 70 m

Accoding to Boyle's law $(P_1{V}_1{)}_{bottom}$ = $(P_2{V}_2{)}_{top}$
(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 $\times$ 8 ${r_1}^3$ $\therefore$ 10 + h = 80 $\therefore$ h = 70 m