Two stones of masses m and 3m are whirled in horizontal circles, the heavier one in a radius r 3 and the lighter one in radius r . When both the stones experience same centripetal forces, the tangential speed of lighter stone is ' n ' times that of the value of heavier stone. The value of ' n ' is

Step-by-step solution

Let the mass, radius, and tangential speed of the lighter stone be m₁ = m , r₁ = r , and v₁ respectively. Let the mass, radius, and tangential speed of the heavier stone be m₂ = 3m , r₂ = r 3 , and v₂ respectively. The centripetal force on the lighter stone is F₁ = m₁ v₁^2 r₁ = m v₁^2 r . The centripetal force on the heavier stone is F₂ = m₂ v₂^2 r₂ = 3m v₂^2 r 3 = 9m v₂^2 r . Given that both stones experience the same centripetal force, F₁ = F₂ . m v₁^2 r = 9m v₂^2 r v₁^2 = 9 v₂^2 v₁ = 3 v₂ Since the tangential sp