Gravitational Potential Energy

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Change in potential energy moving mass m from r₁ to r₂ (r₂ > r₁)?

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-GMm (1/r₂ - 1/r₁)

GMm (1/r₂ - 1/r₁)

GMm (r₂ - r₁)

-GMm (r₂ - r₁)/r₁ r₂

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About This Question

Subject: physics
Chapter: gravitation
Topic: gravitational potential energy
Difficulty: Medium
Year: 2025

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Correct Answer:

GMm (1/r₂ - 1/r₁)

Potential Energy Formula: $U (r) = - \frac{GM m}{r}$ .
Change in Energy ((\Delta U)): $Δ U = U_{f ina l} - U_{ini t ia l} = U (r_{2}) - U (r_{1})$ .
Calculation: $Δ U = (- \frac{GM m}{r _{2}}) - (- \frac{GM m}{r _{1}}) = \frac{GM m}{r _{1}} - \frac{GM m}{r _{2}}$ .
Factor out GMm: $Δ U = GM m (\frac{1}{r _{1}} - \frac{1}{r _{2}})$ .
Sign Check: If $r_{2} > r_{1}$ , then $1/ r_{1} > 1/ r_{2}$ , making $Δ U$ positive. This makes sense as work must be done against gravity to increase separation.

This medium difficulty physics question is from the chapter gravitation, covering the topic of gravitational potential energy. It appeared in the 2025 exam.

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Gravitational Potential Energy

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