A simple pendulum has a periodic time ' T ₁ ' when it is on the surface of earth of radius ' R '. Its periodic time is ' T₂ ' when it is taken to a height ' R ' above the earth's surface. The value of T₂ T₁ is

Step-by-step solution

T ₁=2 l ~g At a height ' h=2 R ' from earth's surface, aligned & T ₂=2 l ~g _ h & ~T ₂ ~T ₁ = g ~g _ h ...(i) & Now, g _ h = GM ( R + h )^2 & ~g _ h = GM 4 R ^2 & ~g _ h = g 4 .( R + h =2 R ) & ( (ii) aligned From equations (i) and (ii), T₂ T₁ = g g / 4 =2