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The approximate formula $mgh$ for gravitational potential energy can be used only when:
AThe object is at infinite distance from the Earth
BThe height $h$ is much larger than the Earth's radius
CThe height $h$ is small compared to the Earth's radius
DThe object's mass is very large
Answer & Solution
Correct answer: C. The height $h$ is small compared to the Earth's radius
1. The formula $mgh$ assumes $g$ is constant over the height $h$.
2. The value of $g$ decreases as height increases, so this is only valid when $h$ is small.
3. When $h$ is small compared with the Earth's radius $R$, $g$ is nearly constant and $mgh$ holds.
4. For large $h$ the exact form $-\dfrac{GMm}{R+h}$ must be used, ruling out the large-$h$ options.
_Source: Balbharati (Maharashtra Board) Class 10 Science & Technology, Ch 1 "Gravitation", p.22_
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