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(A) The relationship between a conservative force and potential energy is given by $F_{	ext{cons}} = -\frac{dU}{dx}$.This implies $F_{	ext{cons}} \c

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by the system against a conservative force.

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(A) The relationship between a conservative force and potential energy is given by $F_{	ext{cons}} = -\frac{dU}{dx}$.This implies $F_{	ext{cons}} \cdot dx = -dU$.The work done by a conservative force is $W_{	ext{cons}} = \int F_{	ext{cons}} \cdot dx = -\Delta U$.Therefore,$\Delta U = -W_{	ext{cons}}$.If work is done by the system against a conservative force,the external work done is positive,which results in an increase in the potential energy of the system $(\Delta U > 0)$.

Column-$I$	Column-$II$
$(1)$ Conservative force	$(a)$ Frictional force
$(2)$ Non-conservative force	$(b)$ Gravitational force
	$(c)$ Internal force

The potential energy of a system increases if work is done

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