In a vehicles lifter, the enclosed gas exerts a force F on a small piston of 8 ~cm diameter. The pressure is transmitted to a second piston of diameter 24 ~cm . If the mass of the vehicle to be lifted is 1400 ~kg , then F must at least be (g=10 ~ms ⁻² )

Step-by-step solution

Given, force on small piston, F₁=F Diameter of small piston, d₁=8 ~cm Mass of vehicle placed on large piston (lift), M=1400 ~kg Diameter of large piston, d₂=24 ~cm By using Pascal's law, Equal pressure will be transmitted from small piston to lift aligned p & = F₁ A₁ = F₂ A₂ F d₁^2 4 = M g d₂^2 4 F & =M g ( d₁ d₂ )^2=1400 10 ( 8 24 )^2 & =1556 ~N & 1600 ~N aligned