An air bubble released at the bottom of a lake, rises and in reaching the top, its radius is 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 in reaching

1.	An air bubble released at the bottom of a lake, rises and in reaching the top, its radius is 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» Solution :Volume of the air bubble at the bottom of the lake `(V_(1))=4/3pir^(3)` Volume of the air bubble at the surface of the lake `(V_(2))=4/3pi(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)(4/3pir^(3))=H[4/3pi(2r)^(3)], (H+h)=8H, h=7H`