A dentist's chair with a patient in it weighs 1700 N. The output plunger of a hydraulic system begins to lift the chair, when the dentist's foot applies a force of 62.5 N to the input piston. Neglect any height difference between the plunger and the piston. What is the ratio of the radius of the plunger to the radius of the piston? The image illustrates a hydraulic lift system, consisting of an output plunger and an input piston. In this system:1. **Output Plunger**: This is where the person sits. The plunger is part of a closed hydraulic system that supports the weight above it.2. **Input Piston**: Located at the right, where the person is standing. This piston is activated to apply pressure within the hydraulic system.**Explanation**: The person standing applies force on the input piston, which generates a pressure in the hydraulic fluid. This pressure is transmitted uniformly throughout the fluid in the system, according to Pascal's principle. As a result, the output plunger rises, lifting the person seated on it. This demonstrates the principle of force multiplication in hydraulic systems, where a small force applied at the input can lift a larger weight at the output.

Given, a dentist's chair with a patient in it weighs F = 1700 N. The output plunger of a hydraulic system begins to lift the chair when the dentist's foot applies a force of F' = 62.5 N to the input piston. To find the ratio of the radius of the plunger R to the radius of the piston R' Area of plunger = A Area of piston = A' Pressure on plunger = P Pressure on piston = P' Using Pascal's principle, the pressure will remain the same across the plunger and the piston: P=P'FA=F'A'A'A=F'FπR'2πR2=F'FR'2R2=F'FR2R'2=FF'RR'=FF'R'R=170062.5R'R=5.21Answer: 5.21