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Question

# A simple pendulum of length 40 cm oscillates with an angular amplitude of 0.04 rad. Find the speed of the bob when the string makes 0.02 rad with the vertical.

A
4.2 cm/s
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B
3.4 cm/s
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C
6.8 cm/s
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D
13.6 cm/s
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Solution

## The correct option is C 6.8 cm/sGiven:- Lenght of the simple pendulum = 40 cm Angular amplitude = 40 rad.To find:- The speed of the bobSolution:- (a)The angular frequency is ω=√gl=√10m/s20.4m=5s−1The time period is 2πω=2π5s−1=1.26s(b) Linear amplitude=40cm×0.04=1.6cm(c) Angular speed ˙θ=ω√θ20−θ2 ˙θ=(5s−1)√(0.04)2−(0.02)2rad=0.17rad/swhere speed of the bob at this instant V=˙θA=(40cm)×(0.17s)=6.8cm/s.Hence the correct option is C

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