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
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
Show Hint
At equilibrium, the force acting on a system is zero, which corresponds to a zero potential energy in this case.
Updated On: Jan 6, 2026
- zero
- \( \frac{MN}{4} \)
- \( \frac{MN^2}{4} \)
- zero
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The Correct Option is D
Solution and Explanation
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).
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