Question

Suppose the gravitational force varies inversely as the nth power of distance .then the time period of a planet in circular orbit of radius R around the sun will be proportional to [AIEEE 2004] ​

Answer 1

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Answer 2

Explanation:- The necessary centripetal force required for a planet to move round the sun = Garvitational force exerted on it

• i.e mv²/r = GMₑm/R
• ⟹ v = (GMₑ/Rⁿ⁻¹)^½____(i)

Now., we know that ,

T = 2πR/V = 2πR × (Rⁿ⁻¹/GMₑ)^½ _____From (i)

⟹ 2π (R²×Rⁿ⁻¹ /GMₑ)^½

⟹ 2π (Rⁿ⁺¹ /GMₑ)^½

⟹ T∝ R(ⁿ⁺¹)/2 Answer