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

Step-by-step solution

For a string, Frequency of vibration n= 1 2 l ~T ~m If T = Mg , then n = 1 2 l Mg m If l₁ and g₁ are the length and acceleration due to gravity at the poles and l₂ and g₂ at the equator respectively, then if the frequency is the same, array ll & n = 1 2 l₁ Mg ₁ ~m = 1 2 l₂ Mg ₂ ~m & ~g ₁ l₁ = g ₂ l₂ or l₂ l₁ = g ₂ ~g ₁ & ~g ₂ g ₁ & l₂ l₁ array