Question

A simple pendulum of length l is set in motion such that the bob, of mass m, moves along a horizontal circular path, and the string makes a constant angle θ with the vertical. The time period of rotation of the bob is t and the tension in the thread is T.

(a) t = 2π√l/g

(b) t = 2π√(lCos θ/g)

(c) T = (4π² ml )/ t²

(d) The bob is in equilibrium.

Answer 1

Correct Answer is: (b) (c) 

Tsin θ = mω²r=  mω² lsin θ or T = mω² l.

Tcos θ = mg or mω² lcos θ = mg or ω² = g/lCos θ.

t = 2π/ω = 2π √lCos θ /g.

T = m [4π² /t²] l.