Introduction:
In this question, we are given two bars of different materials but the same size that are subjected to the same tensile force. We are also given that the unit elongation of the bars is in the ratio of 2:5. We need to determine the ratio of the modulus of elasticity of the two materials.

Modulus of Elasticity:
The modulus of elasticity, also known as Young's modulus, is a measure of the stiffness of a material. It determines the ratio of stress to strain within the elastic limit of a material. It is denoted by the symbol E and has units of force per unit area (Pascal).

Given:
- Unit elongation ratio: 2:5

Explanation:
To find the ratio of the modulus of elasticity, we can use the formula for strain:
strain = change in length / original length

From the given information, we can assume that the original length of both bars is the same. Let's denote the original length as 'L'. The unit elongation ratio tells us that for every 2 units of elongation in the first bar, there are 5 units of elongation in the second bar.

Therefore, we can write the following equations:
strain1 = 2L / L = 2
strain2 = 5L / L = 5

Since the tensile force is the same for both bars, the stress in each bar will also be the same. Let's denote the stress as 'σ'.

Now, we can use the formula for stress:
stress = force / area

Since the cross-sectional area of both bars is the same and the force is the same, the stress in both bars will be equal.

Next, we can use the definition of Young's modulus to find the ratio of the modulus of elasticity:

E = stress / strain

For the first bar:
E1 = σ / strain1 = σ / 2

For the second bar:
E2 = σ / strain2 = σ / 5

Taking the ratio of E2 to E1:
E2 / E1 = (σ / 5) / (σ / 2) = 2 / 5

Conclusion:
The ratio of the modulus of elasticity of the two materials is 2:5.