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Question

A simple pendulum consists of a 50 cm long string connected to a 100 g ball. The ball is pulled aside so that the string makes an angle of 37° with the vertical and is then released. Find the tension in the string when the bob is at its lowest position.

Figure


Solution

From the figure,



cos θ=OCOBOC=OB cos θ=0.5×0.8=0.4So, CA=0.5-0.4=0.1 m

Total energy at A = Total energy at B

12mν2=mg ACν2=2×10×0.1=2v=2

So, the tension is given by

T=mν2r+mg=0.1 20.5+10=1.4 N

Physics
HC Verma - I
Standard XI

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