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Question

# A simple pendulum is oscillating in a vertical plane. If resultant acceleration of bob of mass m at a point A is in horizontal direction, find the tangential force at this point in terms of tension (T) and weight of pendulum (mg).

A
T+mg
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B
mgTT2(mg)2
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C
mgT(mg)2+T2
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D
Tmg(mg)2+T2
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Solution

## The correct option is B mgT√T2−(mg)2When the net acceleration of bob is in horizontal direction at point A , net vertical force on the bob will be zero. Tcosθ−mg=0 ⇒cosθ=mgT ........(1) The tangential force at that instant is F=mgsinθ=mg√1−cos2θ F=mgT√T2−(mg)2 [ from (1) ]

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