Two particles are moving in uniform circular motion in circles of radii R₁ and R₂ . If they experience the exact same magnitude of centripetal acceleration, the ratio of their time periods of revolution ( T₁:T₂ ) will be:

Step-by-step solution

The centripetal acceleration of a particle in uniform circular motion is given by a_ c = ²r . Since = 2 T , we can write a_ c = 4 ² T² r . Given that the centripetal accelerations are equal ( a_ c1 = a_ c2 ): 4 ² T₁² R₁ = 4 ² T₂² R₂ T₁² T₂² = R₁ R₂ T₁ T₂ = R₁ R₂ Thus, the ratio of their time periods is R₁ : R₂ . Answer: R₁ : R₂