It will weigh minimum when an object is placed at : At the center of the Earth, the acceleration due to gravity (g) is zero because the gravitational forces from all parts of the Earth cancel out. In an orbiting satellite, an object is in a state of continuous freefall around the Earth, resulting in apparent weightlessness, which means the object feels minimum (essentially zero apparent) weight.
The weight of any object is felt due to gravity of Earth. When any object goes inside the Earth or above the Earth, weight decreases.
Asked in UPSC CAPF 2014 · Topic: Mechanics (Gravitation and Central Force Motion (Kepler's Laws))
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