A heavy particle hanging from a string of length l is projected horizontally with speed gl . The speed of the particle at the point where the tension in the string equals weight of the particle is

T-mg cos θ = mv2RGiven T = mgmg-mg cos θ = mv2Rg(1-cos θ) = v2R--------------(i)C.O.M.E. at A and B ; ∆K + ∆U = 0(12mv2-12mu2) + mg(R-R cos θ) = 0⇒v2-u2 = -2gR(1-cos θ)⇒v2-(gl)2 = -2v23v2 = gl   ⇒ v = gl3