Question

# A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limit −ϕ and +ϕ. For an angular displacement θ(|θ|<ϕ), the tension in the string and the velocity of the bob are T and V respectively. The following relations hold good under the above conditions:

A
Tcosθ=Mg
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B
TMgcosθ=MV2L
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C
The magnitude of the tangenial acceleration of the bob |aT|=gsinθ
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D
T=Mgcosθ
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Solution

## The correct option is C The magnitude of the tangenial acceleration of the bob |aT|=gsinθSince the body is moving in a circular path, therefore it needs centripetal force (Mv2L). ∴T−Mgcosθ=Mv2L Also, the tangential acceleration acting on the mass is gsinθ.

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