The principle of operation of a hydraulic lift is

Options

A. Boyle's law
B. Pascal's law
C. Newton's law of gravitation
D. Dalton's law of partial pressure

Answer

### Step-by-Step Solution:

1. **Understanding the Hydraulic Lift**:
A hydraulic lift operates based on the principles of fluid mechanics, specifically Pascal's law. It consists of two connected cylinders filled with hydraulic fluid, where one cylinder has a smaller radius (r) and the other has a larger radius (R).

2. **Applying Pascal's Law**:
According to Pascal's law, when pressure is applied to a confined fluid, the pressure change occurs uniformly throughout the fluid. This means that if pressure (P) is changed at any point in the fluid, it will be transmitted equally to all other points in the fluid.

3. **Defining Pressure**:
Pressure (P) is defined as force (F) per unit area (A). For the smaller radius (r), the pressure can be expressed as:
\[ P = \frac{F}{\pi r^2} \]
For the larger radius (R), the pressure can similarly be expressed as:
\[ P = \frac{F'}{\pi R^2} \]

4. **Setting the Pressures Equal**:
Since the pressure is the same in both sections due to Pascal's law, we can set these two equations equal to each other:
\[ \frac{F}{\pi r^2} = \frac{F'}{\pi R^2} \]

5. **Solving for the Output Force (F')**:
By rearranging the equation, we can solve for the output force (F'):
\[ F' = \frac{R^2}{r^2} \cdot F \]
This shows that if the radius of the larger cylinder (R) is greater than the radius of the smaller cylinder (r), then the output force (F') will be greater than the input force (F).

6. **Conclusion**:
The principle of operation of a hydraulic lift is based on Pascal's law, allowing a small input force applied over a small area to be transformed into a larger output force over a larger area. This is why hydraulic lifts can lift heavy loads with relatively little effort.