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

• A. Rⁿ
• B. R⁽ⁿ⁻¹⁾/⁽²⁾
• C. R⁽ⁿ⁺¹⁾/⁽²⁾
• D. R⁽ⁿ⁻²⁾/⁽²⁾

Hint:

Always combine force law with centripetal force for orbital motion.

Answer 1

The Correct Option is C

Step 1: Force: F (1)/(Rⁿ)
Step 2: Equating centripetal force: (mv²)/(R) (1)/(Rⁿ) v R⁽¹⁻ⁿ⁾/⁽²⁾
Step 3: Time period: T = (2π R)/(v) R⁽ⁿ⁺¹⁾/⁽²⁾