Final answer:
In a hydraulic system, the pressure is the same at all points. Using the radii given, we first compute the pressure at the small piston by dividing the force (weight) by the area of the piston. Then using the same pressure, we find out the weight the large piston can support by multiplying the pressure and its area.
Step-by-step explanation:
The question is about the principle of hydraulic machines where pressure applied at one point is transmitted to another point with no change in magnitude. In this scenario, the 10 n weight on the small piston will create a certain pressure, which will be the same on the large piston. First, let's find the pressure on the small piston. Pressure is calculated as force divided by area, and the area of a circle is given by π(radius)². So the pressure from the small piston (P1) is the force (F1: 10n weight) divided by the area of small piston (A1: π(0.1m)²).Following the principle of hydraulic systems, this will be the same pressure experienced at the large piston. Therefore, we can find the force exerted at the large piston (F2) by multiplying this same pressure (P1) by the area of the large piston (A2: π(0.5m)²).
This will give us the weight that the large piston can support.
Learn more about Hydraulic Machines