A frictionless wire 𝐴𝐵 is fixed on a sphere of radius 𝑅. A very small spherical ball slips on this wire. The time taken by this ball to slip from 𝐴 to 𝐵 is

Question : A frictionless wire 𝐴𝐵 is fixed on a sphere of radius 𝑅. A very small spherical ball slips on this wire. The time taken by this ball to slip from 𝐴 to 𝐵 is

(A) \dfrac{2\sqrt{gR}}{g\cos \theta }

(B) 2\sqrt{gR}\cdot \dfrac{\cos \theta }{g}

(C) 2\sqrt{\dfrac{g}{R}}

(D) \dfrac{gR}{g\cos \theta }

Answer : option (C)

Solution :

A frictionless wire 𝐴𝐵 is fixed on a sphere of radius 𝑅. A very small spherical ball slips on this wire. The time taken by this ball to slip from 𝐴 to 𝐵 is
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