A pendulum bob of mass m is suspended at rest. A constant horizontal force F = mg /2 starts acting on it. The maximum angular deflection of the string is

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Let at angular deflection its velocity be v then by work energy theorem W = ᐃKE
mv² = - mg (l - l cosθ) + Fl sinθ
At maximum angular deflection, v = 0
0 = - mg l(1 - cosθ) + sin θ ⇒ 2 - 2 cos ⇒ = sin 4 + 4 cos²θ- 8 cosθ = sin²θ
= 1 - cos²θ
⇒ 5cos²θ - 8 cos θ + 3 = 0 ⇒ 5 cos²θ - 5 cosθ - 3cosθ + 3 = 0
⇒ cos θ = or cosθ = 1⇒ θ = 37^o or = 0^o

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