A hydraulic lift works based on Pascal's principle, which states that the pressure applied at one point in an incompressible fluid is transmitted equally in all directions.

The force exerted by the car on the hydraulic fluid is equal to the weight of the car, which is $$F = mg$$, where $$m$$ is the mass of the car and $$g$$ is the acceleration due to gravity.

Substituting the given values, we get:

$$F = 5000 \, \text{kg} \times 10 \, \text{m/s}^2 = 50000 \, \text{N}$$

The pressure exerted by the car on the hydraulic fluid is equal to the force divided by the area over which the force is distributed, which is $$P = \frac{F}{A}$$, where $$A$$ is the cross-sectional area of the cylinder carrying the load.

However, the given area is in cm², so we need to convert it to m². We know that 1 m² = 10,000 cm², so:

$$A = 250 \, \text{cm}^2 \times \frac{1 \, \text{m}^2}{10000 \, \text{cm}^2} = 0.025 \, \text{m}^2$$

Substituting the values of force and area into the formula for pressure, we get:

$$P = \frac{50000 \, \text{N}}{0.025 \, \text{m}^2} = 2 \times 10^6 \, \text{Pa}$$