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  4. A simple pendulum is oscillating with an angular amplitude 60° . If mass of bob is 50 gram, the tension in the string at mean position is ( g =10 ms -2)

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Q. A simple pendulum is oscillating with an angular amplitude $60^{\circ} .$ If mass of bob is $50\, gram,$ the tension in the string at mean position is $\left( g =10\, ms ^{-2}\right)$

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Solution:

Tension$ T=m g+\frac{m v^{2}}{r}=m g+\frac{m}{l}[2 g l(1-\cos \theta)]$
$=m g+2 m g(1-\cos \theta)=m g+\frac{2 m g}{2}=2 m g$
$=2\left(50 \times 10^{-3}\right)(10)=1 N$