Final answer:
The option that is not correct based on the law of conservation of mechanical energy is 'b. K + U = 0', as this does not reflect that the total mechanical energy is conserved.
Step-by-step explanation:
The question is based on the law of conservation of mechanical energy, which in a closed system in the absence of non-conservative forces (like friction or air resistance), states that the total mechanical energy remains constant. The mechanical energy (E) of a system is the sum of its kinetic energy (K) and potential energy (U). When looking at the provided options, the correct expressions that reflect the law of conservation of mechanical energy are that mechanical energy (E) is the sum of kinetic and potential energy, expressed as E = K + U, and the change in mechanical energy being zero in a closed system if no work is done by non-conservative forces (ΔE = 0).
Therefore, the option that is not correct according to the law of conservation of mechanical energy is 'b. K + U = 0' since this implies that the sum of kinetic and potential energy is zero, which is generally not the case.
The other expressions, like 'a. E = K + U', 'c. ΔK + ΔU = 0' (reflecting that changes in kinetic and potential energy sum up to zero), and 'd. ΔE = 0' (implying that the change in total mechanical energy is zero), all agree with the law of conservation of mechanical energy.