Two simple pendulums of lengths L₁ and L₂ have periodic time T₁ and T₂ respectively (T₁ > T₂) . The time period of the pendulum of length (L₁-L₂) is [(L₁-L₂) > 60 cm ]

Step-by-step solution

The time period of a simple pendulum of length L is given by T = 2 L g . Squaring both sides gives T^2 = 4 ^2 L g , which implies L = g T^2 4 ^2 . For the first pendulum, L₁ = g T₁^2 4 ^2 . For the second pendulum, L₂ = g T₂^2 4 ^2 . The length of the new pendulum is L' = L₁ - L₂ . Substituting the values of L₁ and L₂ gives L' = g 4 ^2 (T₁^2 - T₂^2) . The time period T' of the new pendulum is T' = 2 L' g . Substituting L' gives T' = 2 g(T₁^2 - T₂^2) 4 ^2 g = T₁^2 - T₂^2 . Answer: T₁^2 - T₂^2