Two particles of masses m₁ and m₂ are moving in concentric circles of radii r₁ and r₂ respectively. It is given that the ratio of their masses is m₁ : m₂ = 1 : 2 and the ratio of their radii is r₁ : r₂ = 4 : 1 . If they have the same time period of revolution, the ratio of their centripetal forces F₁ : F₂ is:

Step-by-step solution

Time period T is the same for both particles, so their angular velocity = 2 T is also the same. The centripetal force is given by F = m r ^2 . The ratio of their centripetal forces is: F₁ F₂ = ( m₁ m₂ ) ( r₁ r₂ ) ( ₁ ₂ )^2 Substitute the given values: F₁ F₂ = ( 1 2 ) ( 4 1 ) (1)^2 F₁ F₂ = 2 1 Thus, the ratio F₁ : F₂ is 2 : 1 . Answer: 2 : 1