When the only external force acting is gravity there is a direct correlation between:

Question

BlackTom AI · Accepted Answer

The question asks about the relationships that hold when the only external force is gravity. 
Option a: 'Kinetic and potential energy' – This is the core idea of mechanical energy conservation under gravity. In a system with only conservative gravity, total mechanical energy (kinetic plus potential) remains constant, and energy continuously exchanges between KE and PE as the object moves. This creates a direct, clean correlation: as one form increases, the other decreases correspondingly, keeping the sum constant. 
Option b: 'Potential energy and work' – While there is a relationship between work and potential energy (the work done by gravity equals the negative change in gravitational potential energy, W_gravity = -ΔU), this phrasing is less direct as a primary correlation for the scenario described. It emphasizes work and energy change rather than the exchange between KE and PE that dominates the system’s behavior under gravity alone. 
Option c: 'Power and work' – Power is the rate at which work is done (P = dW/dt). Although related, this option points to a rate concept rather than the energy-form correspondence central to motion under gravity. It does not capture the essential energy-trading relationship that defines the system's dynamics. 
Option d: 'Kinetic energy and power' – Power relates to how quickly kinetic energy changes, but this is not the direct, defining correlation when only gravity acts. It describes the rate of energy change rather than the primary energy forms themselves and their direct exchange. 
To recap, the most fundamental and direct connection in a gravity-only scenario is the interconversion between kinetic and potential energy, governed by mechanical energy conservation. The other options describe valid relationships in different contexts, but they do not embody the primary, direct correlation emphasized by gravity-alone motion.

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