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Questions  

The bob of a pendulum of length l is pulled aside from its equilibrium position through an angle θ and then released. The bob will then pass through its equilibrium position with a speed v, where v equals

a
2gl1-sinθ
b
2gl(1+cosθ)
c
2gl(1−cosθ)
d
2gl(1+sinθ)

detailed solution

Correct option is C

If suppose bob rises up to a height h as shown then after releasing potential energy at extreme position becomes kinetic energy of mean position⇒mgh=12mvmax2⇒vmax=2ghAlso, from figure cosθ=l−hl⇒h=l(1−cosθ)So, vmax=2gl(1−cosθ)

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