A cylindrical cork of uniform density floats in a liquid of density ₁ . If the cork is depressed slightly and released, it oscillates harmonically with time period T. If the same cork floats in another liquid of density ₂ , then the similar oscillation has time period 2T. The value of ₂/ ₁ is :

Step-by-step solution

Let m be the mass of the cork and A be its cross-sectional area. When the cork is depressed by a small distance x in a liquid of density _L , the extra buoyant force provides the restoring force: F = -A _L g x The acceleration of the cork is: a = - A _L g m x Comparing this with the standard equation of SHM a = - ^2 x , we get: = A _L g m The time period of oscillation is: T = 2 = 2 m A _L g This shows that T 1 _L . For the first liquid of density ₁ : T 1 ₁ For the second liquid of density ₂ : 2T 1 ₂ Dividing the t