Question

When an air bubble of radius r rises from the bottom to the surface of a lake, its radius becomes `(5r)/4`. Taking the atmospheric pressure to be equal to the 10 m height of the water column, the depth of the lake would approximately be ______.

(ignore the surface tension and the effect of temperature)

Options

• 10.5 m

• 8.7 m

• 11.2 m

• 9.5 m

Answer 1

When an air bubble of radius r rises from the bottom to the surface of a lake, its radius becomes `(5r)/4`. Taking the atmospheric pressure to be equal to the 10 m height of the water column, the depth of the lake would approximately be 9.5 m.

Explanation:

Using `P_1V_1 = P_2V_2`

`(P_1)4/3pir^3 = (P_2)4/3pi(125r^3)/64`

`(rhog(10) + rhogh)/(rhog(10)) = 125/64` ⇒ 640 + 64h = 1250

On solving we get h = 9.5 m