If the length of the oscillating simple pendulum is made 1 3 times the original keeping amplitude same then increase in its total energy at a place will be

Step-by-step solution

The total energy of an oscillating simple pendulum is E = 1 2 m ^2 A^2 where m is mass, is angular frequency, and A is amplitude. For a simple pendulum, = g L where g is gravitational acceleration and L is length. Substituting, E = 1 2 m ( g L )^2 A^2 = 1 2 m g A^2 L . With original length L₁ , the energy is E₁ = 1 2 m g A^2 L₁ . When the length is reduced to L₂ = L₁ 3 with amplitude unchanged, the new energy becomes E₂ = 1 2 m g A^2 L₂ = 1 2 m g A^2 L₁/3 = 3 2 m g A^2 L₁ = 3E₁ . The increase in total energy is E₂