The ratio of the frequencies of two simple pendulums is 4: 3 at the same place. The ratio of their respective lengths is

Step-by-step solution

The frequency of a simple pendulum is given by f = 1 2 g L , where g is constant for both pendulums at the same location. For two pendulums with frequencies f₁ , f₂ and lengths L₁ , L₂ , the frequency ratio simplifies to: f₁ f₂ = L₂ L₁ Given f₁ : f₂ = 4 : 3 , we have 4 3 = L₂ L₁ . Squaring both sides yields ( 4 3 )^2 = L₂ L₁ , so 16 9 = L₂ L₁ . The length ratio is therefore L₁ : L₂ = 9 : 16 . Final answer: C