The areas of pistons in a hydraulic machine are `5cm^(2)` and `625 cm^(2)`. What force on the smaller piston will support a load of `1250` N on the larger piston ? State any assumption which you make in your calculation.

Answer

To solve the problem, we will use Pascal's law, which states that the pressure applied to a confined fluid is transmitted undiminished in every direction throughout the fluid. This means that the pressure on the smaller piston (P1) is equal to the pressure on the larger piston (P2).

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Area of the smaller piston (A1) = 5 cm²
- Area of the larger piston (A2) = 625 cm²
- Force on the larger piston (F2) = 1250 N

2. **Write the Formula for Pressure**:
According to Pascal's law, the pressure on both pistons is equal:
\[ P_1 = P_2 \]
Where pressure (P) is defined as:
\[ P = \frac{F}{A} \]
Thus, we can write:
\[ \frac{F_1}{A_1} = \frac{F_2}{A_2} \]

3. **Substitute the Known Values**:
Substitute the known values into the equation:
\[ \frac{F_1}{5 \, \text{cm}^2} = \frac{1250 \, \text{N}}{625 \, \text{cm}^2} \]

4. **Calculate the Right Side**:
Simplify the right side:
\[ \frac{1250 \, \text{N}}{625 \, \text{cm}^2} = 2 \, \text{N/cm}^2 \]

5. **Set Up the Equation**:
Now we have:
\[ \frac{F_1}{5 \, \text{cm}^2} = 2 \, \text{N/cm}^2 \]

6. **Solve for F1**:
Multiply both sides by 5 cm² to find F1:
\[ F_1 = 2 \, \text{N/cm}^2 \times 5 \, \text{cm}^2 = 10 \, \text{N} \]

### Final Answer:
The force on the smaller piston (F1) that will support a load of 1250 N on the larger piston is **10 N**.

### Assumption:
We assume that the pistons are frictionless, allowing for the ideal transmission of pressure without any loss.