The potential energy of a system increases if work is done:

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Accepted Answer

1. **Definition:** The change in potential energy ($\Delta U$) is defined as the negative of the work done by the conservative force ($W_c$).
   $$ \Delta U = -W_c $$ [Class 11 Physics, Ch 6, Sec 5.7, Eq 5.7]
2. **Analysis:** For the potential energy to increase ($\Delta U > 0$), the work done *by* the conservative force ($W_c$) must be negative.
3. **Interpretation:** Negative work done by a force implies that the displacement is opposite to the direction of the force. This is equivalent to saying that work is being done **against** the conservative force (e.g., lifting a mass against gravity increases its gravitational potential energy).

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