At the poles, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator, for same setting to produce resonance with same fork, the vibrating length of wire

Step-by-step solution

(A) Frequency of vibration n = 1 2 e T m If T = Mg , then n = 1 2 e Mg m If ₁ and g ₁ are length and acceleration due to gravity at the pole and ₂ and g ₂ at the equator then, if frequency is same, then n= 1 2 ₁ M g₁ m = 1 2 ₂ M g₂ m g₁ ₁ = g₂ ₂ or ₂ ₁ = g₂ g₁ g ₂ < g ₁ ₂ < ₁