Time period of a simple pendulum is T₁ when on the earth's surface and T₂ when taken to a height '2R' above the earth's surface, where 'R' is the radius of the earth. The ratio T₁ : T₂ is

Step-by-step solution

The time period of a simple pendulum is given by T = 2 L g . The acceleration due to gravity at a distance r from the center of the earth is g = GM r^2 . Substituting this into the time period formula gives T = 2 L r^2 GM , which implies T r . On the surface of the earth, the distance from the center is r₁ = R , so T₁ R . At a height h = 2R above the surface, the distance from the center is r₂ = R + 2R = 3R , so T₂ 3R . The ratio of the time periods is T₁ T₂ = R 3R = 1 3 . Thus, T₁ : T₂ = 1 : 3 . Answer: 1 : 3