The gravitational potential energy of a system of two point masses m₁ and m₂ separated by distance r is taken to be zero at infinite separation. At finite r the PE is:
AU = −G m₁ m₂ / r
BU = +G m₁ m₂ / r
CU = −G m₁ m₂ / r²
DU = ½ G m₁ m₂ / r
Answer & Solution
Correct answer: A. U = −G m₁ m₂ / r
1. Work done by gravity in bringing m₂ from infinity to a separation r is positive (gravity attracts).
2. Since U(∞) = 0, the PE at finite r is the NEGATIVE of that work.
3. U(r) = −G m₁ m₂ / r.
4. The negative sign shows the system is bound; energy must be supplied to separate the masses.
5. The −1/r² choice confuses PE with force; PE scales as 1/r, not 1/r².
_Source: NCERT Class 11 Physics Ch 7 "Gravitation", §7.7 Gravitational PE_
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