Question

A classical particle has total energy \( E \). The plot of potential energy \( U(r) \) as a function of distance \( r \) from the centre of force located at \( r = 0 \) is shown in the figure. Which of the regions are forbidden for the particle? 

• A. I and II
• B. II and IV
• C. I and IV
• D. I and III

Hint:

In potential energy graphs, regions where the potential energy exceeds the total energy are forbidden for the particle, as it cannot exist in these regions.

Answer 1

The Correct Option is D

Step 1: Analyzing the potential energy graph.
From the given graph, we observe the potential energy \( U(r) \) as a function of distance \( r \). The particle's total energy \( E \) is constant, and we can compare it with the potential energy at different points on the graph.

Step 2: Identifying forbidden regions.
For regions where the potential energy exceeds the total energy, the particle cannot exist there. This is because the total energy \( E \) represents the maximum potential energy the particle can have. The regions where the potential energy \( U(r) \) is greater than \( E \) correspond to forbidden regions. These are the regions labeled II and IV.
Step 3: Conclusion.
Therefore, the forbidden regions for the particle are in the regions labeled II and IV, where the potential energy is greater than the total energy.