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

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When an air bubble of radius r rises from the bottom to the surface of a lake, its radius becomes 5 r 4 . Taking the atmospheric pressure to be equal to 10 ~m height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature):

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Correct answer: D. 9.5 ~m

Using P ₁ ~V ₁= P ₂ ~V ₂ aligned & (P₁ ) 4 3 r^3= (P₂ ) 4 3 125 r^3 64 & g(10)+ g h g(10) = 125 64 &640+64 h=1250 aligned On solving we get h=9.5 ~m

When an air bubble of radius r rises from the bottom to the surface of a lake, its radius becomes 5 r 4 . Taking the atmospheric pressure to be equal to 10 ~m height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature):

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