A hydraulic lift is designed to lift a heavy vehicle of mass 2000 kg . A force of 200 N is applied on the smaller piston. If the diameter of the smaller piston is 5 cm , the required diameter of the larger piston to maintain equilibrium is _____ cm . (Take g = 10 m/s ^2 )

Step-by-step solution

According to Pascal's law, the pressure applied on the smaller piston is transmitted undiminished to the larger piston. F₁ A₁ = F₂ A₂ Here, F₁ = 200 N and d₁ = 5 cm . The force required on the larger piston is equal to the weight of the vehicle: F₂ = Mg = 2000 10 = 20000 N Since area is proportional to the square of the diameter ( A d^2 ): F₁ d₁^2 = F₂ d₂^2 200 5^2 = 20000 d₂^2 200 25 = 20000 d₂^2 8 = 20000 d₂^2 d₂^2 = 20000 8 = 2500 d₂ = 50 cm Answer: 50