In which scenario does an object have zero gravitational potential energy with respect to a given reference point?
When the object is at the same level as the reference point
Gravitational potential energy near the Earth's surface is U = mgh, where m is the mass, g is the acceleration due to gravity and h is the height of the object measured from a chosen reference level, where U is taken as zero.
When the object is at the same level as the reference point, its height above that level is h = 0. So U = mg × 0 = 0, and the object has zero gravitational potential energy with respect to that point.
When the object is above the reference point, h is positive and U is positive. Moving horizontally above it does not change h, so U stays positive and the same; horizontal motion only adds kinetic energy.
When the object is below the reference point, h is negative and U = mgh is negative, not zero. Check: for a 2 kg object 3 m above the level, U = 2 × 10 × 3 = 60 J, while at the level itself U = 2 × 10 × 0 = 0 J.
Hence, When the object is at the same level as the reference point.
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