A lake filled with water has depth H, A pipe of length slightly less than H lies at the bottom of the lake. It contains an ideal gas filled up to a length of `(H)/(10)` A smooth an ideal gas filled up to a length gas in place. Now the pipe is slowly raised to vertical position (see figure). Assume that temperature of the gas remains Constant and neglect the atmospheric pressure.

(a) Plot the variation of pressure inside the lake as a function of height y from the base. Let the height of piston frm the base, after the pipe is made vertical, by y. plot the variation of gas pressure as a function of y in the first graph itself.
(b) In equilibrium the gas pressure and the pressure due to water on the piston must be equal. Using this solve for equilibrium height `y_(0)` of the piston. You get two answers. Which one is correct and why?

Answer

(a) `(##IJA_PHY_V01_C08_E01_035_A01##)`
(b) `y=(H)/(2)-sqrt(15)/(10)H`