In a hydraulic press, the area of smaller and larger pistons are `5 cm^(2) and 20 cm^(2)`, respectively. Calculate the weight which can be raised by larger piston if a force of 100 kgf is applied on smaller piston.

Answer

To solve the problem of calculating the weight that can be raised by the larger piston in a hydraulic press, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Area of smaller piston, \( A_1 = 5 \, \text{cm}^2 \)
- Area of larger piston, \( A_2 = 20 \, \text{cm}^2 \)
- Force applied on the smaller piston, \( F_1 = 100 \, \text{kgf} \)

2. **Convert the Force to Newtons:**
- Since \( 1 \, \text{kgf} \) is equivalent to \( 9.81 \, \text{N} \):
\[ F_1 = 100 \, \text{kgf} \times 9.81 \, \text{N/kgf} = 981 \, \text{N} \]

3. **Calculate the Pressure Exerted on the Smaller Piston:**
- Pressure \( P \) is defined as force per unit area:
\[ P = \frac{F_1}{A_1} \]
- Substituting the values:
\[ P = \frac{981 \, \text{N}}{5 \, \text{cm}^2} \]
- Converting \( 5 \, \text{cm}^2 \) to \( \text{m}^2 \) (since \( 1 \, \text{cm}^2 = 10^{-4} \, \text{m}^2 \)):
\[ A_1 = 5 \times 10^{-4} \, \text{m}^2 \]
- Therefore,
\[ P = \frac{981 \, \text{N}}{5 \times 10^{-4} \, \text{m}^2} = 1962000 \, \text{N/m}^2 \, (\text{Pascals}) \]

4. **Apply Pascal’s Law:**
- According to Pascal's law, the pressure in a hydraulic system is the same at all points. Thus, the pressure on the larger piston \( P \) is also given by:
\[ P = \frac{F_2}{A_2} \]
- Where \( F_2 \) is the force exerted by the larger piston.

5. **Calculate the Force on the Larger Piston:**
- Rearranging the equation for \( F_2 \):
\[ F_2 = P \times A_2 \]
- Substituting the values:
\[ A_2 = 20 \, \text{cm}^2 = 20 \times 10^{-4} \, \text{m}^2 \]
- Therefore,
\[ F_2 = 1962000 \, \text{N/m}^2 \times 20 \times 10^{-4} \, \text{m}^2 = 3920 \, \text{N} \]

6. **Convert the Force on the Larger Piston to kgf:**
- To convert \( F_2 \) back to kgf:
\[ F_2 \text{ (in kgf)} = \frac{3920 \, \text{N}}{9.81 \, \text{N/kgf}} \approx 400 \, \text{kgf} \]

### Final Answer:
The weight that can be raised by the larger piston is approximately **400 kgf**.