If the gravitational force between two bodies were proportional to 1/R instead of 1/R², how would the orbital speed v of a particle in a circular orbit vary with radius R?
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If the gravitational force between two bodies were proportional to 1/R instead of 1/R², how would the orbital speed v of a particle in a circular orbit vary with radius R?

G1 Physics · Accepted Answer

Step 1: With force proportional to 1/R, write F=k/R. Step 2: Centripetal balance mv²/R=k/R gives mv²=k, independent of R; thus v∝R⁰. Final answer: B — R⁰ (independent of R).