The correct option is C 7H
We know, atmospheric pressure Po = ρgH
where ρ is the density of water.
Assuming the depth of the lake be d, the pressure at this depth will be, P = Po+ρgd = ρg(H+d)
Since, the temperature is constant, we can assume that the process takes place isothermally.
So, applying the Boyle's Law
P1V1=P2V2...(i)
where , 1 denotes the water at depth d and 2 denotes the surface of water.
So, P1=ρg(d+H)
at surface, it will be atmospheric pressure i.e P2=ρgH
Volume V = 43πr3
on doubling the radius, the volume will increase to 8 times
i.e V2=8V1
put up the values in equation (i)
Substituting the values, in Boyle's Law,
P1=ρg(d+H)V=ρgH×8V
d=8H−H = 7H