In a solar system, the time-period of revolution of a planet tracing a circular orbit of radius R is proportional to:

Solution & Explanation

Principle: for a planet in a circular orbit the gravitational pull supplies the centripetal force. G·M·m/R² = m·v²/R, where M is the star's mass and v the orbital speed. So v² = G·M/R, giving v = √(G·M/R). The period is T = 2π·R/v = 2π·R/√(G·M/R) = 2π·R·√(R/(G·M)) = 2π·√(R³/(G·M)). Hence T² = (4π²/(G·M))·R³, i.e. T² ∝ R³ (Kepler's third law). Taking the square root, T ∝ R^(3/2). This matches option B, R^(3/2). Trap: R² and R³ correspond to T (not T²); only T² scales as R³, so T itself scales as R^(3/2).