An air bubble released at the bottom of a lake, rises and on reaching the top, its radius found to be doubled. If the atmospheric pressure is equivalent to H metre of water column, find the depth of the lake (Assume that the temperature of water in the lake is uniform)

An air bubble released at the bottom of a lake, rises and on reaching

1.	An air bubble released at the bottom of a lake, rises and on reaching the top, its radius found to be doubled. If the atmospheric pressure is equivalent to H metre of water column, find the depth of the lake (Assume that the temperature of water in the lake is uniform)
Answer» <P> SOLUTION :Volume of the air bubble at the bottom of the lake `(V_(1) ) = (4)/(3) pi r^(3)` Volume of the air bubble at the surface of the lake `(V_(2)) = (4)/(3) pi (2r)^(3)` Pressure at the surface of the lake `(P_(2))`=H METRE of water COLUMN. If .h. is the depth of the lake.the pressure at the bottom of the lake `(P_(1)) `= (H+h) metre of water column. Since the temperature of the lake is uniform, According to Boyle.s LAW, `P_(1) V_(1) = P_(2) V_(2)` `(H + h) ((4)/(3) pi r^(3)) = H [ (4)/(3) pi (2r)^(3) ] ` ( H + h ) = 8Hh = 7H