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Given

Height of vertical cylinder=100cm=1m

Pressure P₁=75cm of Hg=0.75m of Hg

1mm of Hg = hg Pa

Where h= height of mercury column =1mm=0.001m

= density of mercury

g= acceleration due to gravity

So,

P₁= 0.75m of Hg= 0.75g Pa

Let h be height of mercury above the piston. When mercury is poured over piston the piston will move down and gas inside vessel will get compressed.

So, let the pressure of gas when mercury is poured be P₂

So,

P₂=P₁+hg=0.75g+ hg

Let the circular area of cylinder be A.

Then, volume of gas before mercury was poured V₁=Aheight of cylinder

V₁=A1=A

Height of cylinder when mercury was poured =(1-h) m

Volume of gas after mercury was poured V₂=A(1-h)

Since it is given in question that temperature has not being changed so we can apply Boyle’s law which states that PV=constant, if temperature is constant.

P₁V₁=P₂V₂

0.75gA=0.75g+ hg A(1-h)

Taking gA common from both side of equation we get

0.75=(0.75+h) (1-h)

0.75=0.75+h-0.75h-h²

h²-0.25h=0

h-0.25=0h=0.25m

The maximum height of the mercury column that can be put on the piston is 25cm.