Question

A body moves in a circular orbit of radius R under the action of a central force. Potential due to the central force is given by V(r)=kr (where k is a positive constant). Period of revolution of the body is proportional to

• A. R¹/2
• B. R⁻1/2
• C. R⁻3/2
• D. R⁻5/2

Hint:

If the central force is constant (independent of r), then: T ∝ √(R)

Answer 1

The Correct Option is A

Step 1: Given potential: V(r)=kr Force is: F = -(dV)/(dr) = -k So the magnitude of force is constant: F = k 

Step 2: For circular motion, centripetal force: (mv²)/(R) = k ⟹ v² = (kR)/(m) 

Step 3: Angular velocity: ω = (v)/(R) = √((k)/(mR)) 

Step 4: Time period: T = (2π)/(ω) ∝ √(R) boxedT ∝ R¹/2