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If the gravitational attraction between two bodies is inversely proportional to the nth power of their separation, then the period of a planet moving in a circular orbit of radius R around the Sun is proportional to

1. Rⁿ
2. R^((n−1)/2)
3. R^((n+1)/2)
4. R^((n−2)/2)

Correct answer: R^((n+1)/2)

Solution

The period of a planet in a circular orbit is derived from Kepler's third law, which states that the square of the period is proportional to the cube of the semi-major axis of the orbit. When gravitational attraction is inversely proportional to the nth power of the separation, the relationship modifies to show that the period is proportional to R raised to the power of (n+1)/2, reflecting the balance between gravitational force and centripetal force.

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