The given question asks us to determine the stress produced in a bar when a load is applied suddenly compared to when it is applied gradually. Let's analyze the situation step by step.

1. Maximum Stress Produced in a Bar:
The maximum stress produced in a bar when a load is applied suddenly is given as 40 N/mm2. This means that the bar experiences a maximum stress of 40 N/mm2 when the load is suddenly applied.

2. Stress and Load Relationship:
Stress is defined as the force per unit area and is calculated by dividing the load applied by the cross-sectional area of the bar. Mathematically, stress (σ) can be expressed as σ = F/A, where F is the force applied and A is the cross-sectional area.

3. Gradual Load Application:
When the same load is applied gradually, it means that the force is applied over a longer period of time. In this case, the bar has time to deform and adjust to the applied load. As a result, the stress produced in the bar will be lower compared to when the load is applied suddenly.

4. Determining the Stress:
Since the load is applied gradually, the stress produced in the bar can be calculated using the same formula as before, σ = F/A. However, the force applied will be the same as before, but the time taken to apply the load will be longer. Therefore, the value of stress will be reduced.

5. Answer:
Based on the above analysis, the stress produced in the bar when the load is applied gradually will be lower than 40 N/mm2. Among the given options, option 'B' (20 N/mm2) is the correct answer as it represents the reduced stress value.

In conclusion, when a load is applied gradually, the stress produced in a bar is lower compared to when the load is applied suddenly. This is because the bar has time to adjust and deform, reducing the stress in the material.