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Two spheres of mass 2M and M are initially at rest, separated by distance R. Due to mutual gravitational attraction they approach each other. When the separation between them becomes R/2, what is the acceleration of the center of mass of the system?
- Zero
- g m/s²
- 3g m/s²
- Data insufficient
Correct answer: Zero
Solution
The two-sphere system is isolated — there are no external forces. The gravitational attraction is an internal force (Newton's 3rd law pair). Net external force on the system = 0. By Newton's second law for the center of mass: F_net_external = (M_total) * a_CM => 0 = (2M + M) * a_CM => a_CM = 0. The acceleration of the center of mass is zero regardless of separation.
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