In an ideal hydraulic braking system, the master-cylinder piston has area 2 cm². A driver exerts a force of 200 N on it. Each of four identical wheel cylinders has piston area 6 cm². Neglecting all losses, what is the total force exerted by the four wheel-cylinder pistons?
Options

Question

In an ideal hydraulic braking system, the master-cylinder piston has area 2 cm². A driver exerts a force of 200 N on it. Each of four identical wheel cylinders has piston area 6 cm². Neglecting all losses, what is the total force exerted by the four wheel-cylinder pistons?

Options

G1 Physics · Accepted Answer

Pressure produced in the master cylinder is P = F(master)/A(master). By Pascal's law, the same pressure reaches each wheel cylinder. Force on one wheel piston is F(wheel) = P A(wheel) = F(master)A(wheel)/A(master). Therefore, F(wheel) = 200×6/2 = 600 N. There are four identical wheel cylinders. Hence, F(total) = 4×600 = 2400 N. Correct option: D.