Question

If the potential energy of a gas molecule is \[ U = \frac{M}{r} - \frac{N}{r^2} \] where \( M \) and \( N \) are positive constants, then the potential energy at equilibrium must be

• A. zero
• B. \( \frac{MN}{4} \)
• C. \( \frac{MN^2}{4} \)
• D. zero

Hint:

At equilibrium, the force acting on a system is zero, which corresponds to a zero potential energy in this case.

Answer 1

The Correct Option is D

Step 1: Understanding the potential energy formula.
At equilibrium, the potential energy is minimized. By differentiating the given potential energy formula and setting it to zero, we can find the equilibrium condition. The potential energy at equilibrium is zero.

Step 2: Conclusion.
The potential energy at equilibrium is zero. Therefore, the correct answer is option (4).