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Question

# A simple pendulum has a bob of mass m and swings with an angular amplitude ϕ. The tension in the thread is T. At a certain time, the string makes an angle θ with the vertical (θ≤ϕ)

A
T=mgcosθ, for all values of θ
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B
T=mgcosθ, only for θ=ϕ
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C
T=mg, for θ=cos1[13(2cosϕ+1)]
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D
T will be larger for smaller values of θ
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Solution

## The correct options are B T=mg, for θ=cos−1[13(2cosϕ+1)] C T will be larger for smaller values of θ D T=mgcosθ, only for θ=ϕAt any point of time the forces on the bob are Tension , gravitational and the centripetal forceWe have mg(lcosθ−lcosϕ)= 1/2 mv2mv2l= 2mg(cosθ−cosϕ)Also T−mgcosθ=mv2l=2mg(cosθ −cosϕ)or T= mg(3cosθ− 2cosϕ)For θ = cos−113(2cosϕ+1)T=mg

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