A syringe has two cylindrical parts of cross sectional area `A_(1) = 4 cm^(2)` and `A_(2) = 1 cm^(2)`. A mass less piston can slide on the inner wall of the part having cross section `A_(1)`. The end of the part having cross section `A_(2)` is open. Syringe is dipped in a large water tank such that the narrower part remains completely submerged and the wider part is filled with air. The length shown in figure are `h_(1) = 55 cm " and " h_(2) = 100` cm. The piston is pushed down by a distance x such that 25% of the air inside the syringe is expelled out through the open end of the narrower part. Assume that the temperature of air remains constant and calculate x.
Density of water = `10^(3) k gm^(– 3) , g = 10 ms^(– 2)`, Atmospheric pressure = `10^(5) Nm^(–2)`.

Answer

42.5 cm