What should be the ratio of area of cross section of the master cylinder and wheel cylinder of a hydraulic brake so that a force of 15 N can be obtained at each of it’s brake shoe by exerting a force of 0.5 N on the pedal ?

Let,

area of cross section of the master cylinder = A₁

area of cross section of the wheel cylinder = A₂

force applied on pedal be F₁ = 0.5 N

force applied on brake shoe F₂ = 15 N

⇒ {A_1\over A_2 } = {F_1\over F_2}

⇒ {A_1\over A_2 } = {0.5\over 15}

⇒ {A_1\over A_2 } = {5\over 150}

⇒ {A_1\over A_2 } = {1\over 30}

Hence, the ratio of area of cross section = 1 : 30