Work, Power and EnergyHard
Question
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
Options
A.90o
B.53o
C.37o
D.60o
Solution
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 = 37o or = 0o
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 = 37o or = 0oCreate a free account to view solution
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