Masses M1 and M2 are initially separated by a distance Ra. Mass M2 is now moved further away from mass M1 such that their final separation is Rb. Which of the following statements best describes the work Wab done by the force of gravity on M2 as it moves from Ra to Rb?
A. Wab > 0.
B. Wab = 0.
C. Wab < 0.

A. Wab > 0.

Explanation:

Work done will be equal to change in gravitational energy in the whole process .

When Masses M₁ and M₂ are initially separated by a distance Ra

their gravitational energy

= - G M₁ M₂ / Ra

When mass M₂ is now moved further away from mass M₁ such that their final separation is Rb

their gravitational energy

= - G M₁ M₂ / Rb

Change in gravitational energy

= - G M₁ M₂ / Rb - (  - G M₁ M₂ / Ra )

=  G M₁ M₂ / Ra -  - G M₁ M₂ / Rb

=   G M₁ M₂ ( 1 / Ra - Rb )

As Ra < Rb

1/Ra > 1 / Rb

So change in gravitational energy is positive

So

Wab > 0.

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