In a hydraulic machine a force of 0.5N acts normally on the Smaller piston of area 0.1m2. The force that acts on the larger piston whose area is 200m2 will be

The principle at work here is Pascal's law, which states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container.

Step 1: Identify the given values. Force on the smaller piston (F1) = 0.5 N Area of the smaller piston (A1) = 0.1 m² Area of the larger piston (A2) = 200 m²

Step 2: Use Pascal's law to set up the equation. Pascal's law states that the pressure is the same at all points in an incompressible, enclosed fluid. So, the pressure on the smaller piston equals the pressure on the larger piston. We can express this as:

F1/A1 = F2/A2

Step 3: Solve for the unknown. We're trying to find the force on the larger piston (F2). We can rearrange the equation to solve for F2:

F2 = (F1/A1) * A2

Step 4: Substitute the known values into the equation and solve. F2 = (0.5 N / 0.1 m²) * 200 m² = 1000 N

So, the force that acts on the larger piston is 1000 N.