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. \(R^{1/2}\)
• B. \(R^{-1/2}\)
• C. \(R^{-3/2}\)
• D. R⁻5/2

Hint:

For circular motion, always relate force to mv²/R first.

Answer 1

The Correct Option is A

Step 1: Force due to potential F = -(dV)/(dr) = -k
Step 2: For circular motion (mv²)/(R) = k ⟹ v ∝ √(R)
Step 3: Period T=(2π R)/(v) ∝ fracR√(R) = R¹/2