Question

An air bubble doubles in radius on rising from bottom of a take to its surface. If the atmospheric pressure is equal to that due to a column of 10 m of water, then find the depth of the lake assume temperature constant and neglect surface tension -

• A. 50 m
• B. 70 m
• C. 40 m
• D. 20 m

Answer 1

The correct option is B 70 m

$\text{Assuming constant temperature, we use}{P}_1{V}_1=P_2{V}_{2}Given:P_2=\left(10\right)\text{dg (for water column)}{P}_1=(10+h)dg\text{(where h = depth of lake)}{V}_1=\frac{4\pi }{3}{r}^3{V}_2=\frac{4\pi }{3}(2r{)}^3=8.\left(\frac{4\pi }{3}{r}^3\right)=8V_1\text{Thus for}{P}_2{V}_2=P_1{V}_1,\text{we have}10dg(8V_1)=(10+h)dg{V}_{1}or80=10+hh=70m$