Two simple pendulums have first (A) bob of mass ' M₁ ' and length ' L₁ ', second (B) of mass ' M₂ ' and length ' L₂ '. M₁=M₂ and L₁=2 L₂ . If their total energies are same then the correct statement is

Step-by-step solution

The total energy E of a simple pendulum with small angular amplitude ₀ and length L is E = 1 2 m g L ₀^2 . Given equal total energies E_A = E_B , identical masses M₁ = M₂ , and lengths L₁ = 2L₂ , we have: 1 2 M₁ g (2L₂) _ 0A ^2 = 1 2 M₁ g L₂ _ 0B ^2 Cancelling common factors M₁ g L₂ yields 2 _ 0A ^2 = _ 0B ^2 , so _ 0B = 2 _ 0A . The linear amplitudes relate as A = L ₀ , giving A_A = 2L₂ _ 0A and A_B = L₂ 2 _ 0A . The ratio is A_B A_A = 2 2 = 1 2 0.707 , showing A_B Amplitude of B is smaller than amplitude of A.