Question:
The gravitational potential energy of a body of mass m on the surface of earth of mass M and radius R is ________.
The gravitational potential energy of a body of mass m on the surface of earth of mass M and radius R is ________.
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The negative sign indicates that the gravitational force is attractive and work must be done to move the mass to infinity.
Updated On: Jun 26, 2026
- $\frac{-GMm}{R}$
- $\frac{GMm}{R}$
- $mgR$
- $-mgR$
- Zero
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The Correct Option is A
Solution and Explanation
Step 1: Concept
Gravitational potential energy ($U$) is the energy possessed by an object due to its position in a gravitational field.
Step 2: General Formula
For two point masses $M$ and $m$ separated by distance $r$, $U = -\frac{GMm}{r}$.
Step 3: Application to Earth
On the surface of the Earth, the distance from the center of mass is equal to the radius $R$.
Step 4: Conclusion
Substituting $r = R$, we get $U = -\frac{GMm}{R}$. Final Answer: (A)
Gravitational potential energy ($U$) is the energy possessed by an object due to its position in a gravitational field.
Step 2: General Formula
For two point masses $M$ and $m$ separated by distance $r$, $U = -\frac{GMm}{r}$.
Step 3: Application to Earth
On the surface of the Earth, the distance from the center of mass is equal to the radius $R$.
Step 4: Conclusion
Substituting $r = R$, we get $U = -\frac{GMm}{R}$. Final Answer: (A)
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