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The gravitational potential energy of an object of mass $m$ at a height $h$ above the Earth's surface (mass $M$, radius $R$) is given by:
A$+\dfrac{GMm}{R+h}$
B$-\dfrac{GMm}{R+h}$
C$-\dfrac{GMm}{R^2}$
D$+mgh$ for all heights
Answer & Solution
Correct answer: B. $-\dfrac{GMm}{R+h}$
1. Potential energy is taken as zero at infinite distance, where gravity does not act.
2. At finite distances the potential energy is less than zero, i.e. negative.
3. At height $h$ the object's distance from the centre is $R + h$.
4. So the gravitational potential energy is $-\dfrac{GMm}{R+h}$; the positive sign and $mgh$ (valid only for small $h$) are wrong here.
_Source: Balbharati (Maharashtra Board) Class 10 Science & Technology, Ch 1 "Gravitation", p.22_
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