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(C) Mechanical energy $E$ is defined as the sum of kinetic energy $K$ and potential energy $U$,so $E = K + U$. Thus,statement $(A)$ is correct.Mechani

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Work done by a conservative force is always equal to the negative of the change in mechanical energy.

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(C) Mechanical energy $E$ is defined as the sum of kinetic energy $K$ and potential energy $U$,so $E = K + U$. Thus,statement $(A)$ is correct.Mechanical energy is conserved only when only conservative forces do work. If a non-conservative force (like friction) acts on the system,it typically changes the mechanical energy (often dissipating it as heat). Therefore,statement $(B)$ is incorrect.The work done by a conservative force $W_c$ is equal to the negative change in potential energy,i.e.,$W_c = -\Delta U$. Since $\Delta E = \Delta K + \Delta U$,if only conservative forces act,$\Delta E = 0$. Statement $(C)$ claims $W_c = -\Delta E$,which is only true if $\Delta K = 0$. In general,$W_c = -\Delta U$,not $-\Delta E$. Thus,statement $(C)$ is also incorrect.Since both $(B)$ and $(C)$ are incorrect,and the question asks for the incorrect statement,there is an ambiguity in the provided options. However,based on standard physics definitions,$(C)$ is fundamentally incorrect as a general principle.

Select the incorrect statement regarding the mechanical energy of a body/system.

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