# 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) $\dfrac{gR}{g\cos \theta }$