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(B) For a pendulum with angular amplitude $	heta$,the height $h$ reached by the bob is given by $h = l(1 - \cos 	heta)$,where $l$ is the length of t

Vedclass · Accepted Answer

$60$

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(B) For a pendulum with angular amplitude $	heta$,the height $h$ reached by the bob is given by $h = l(1 - \cos 	heta)$,where $l$ is the length of the string.By the law of conservation of energy,the kinetic energy at the mean position is equal to the potential energy at the extreme position:$\frac{1}{2} m v^2 = m g h = m g l(1 - \cos 	heta)$$v^2 = 2 g l(1 - \cos 	heta)$The maximum tension $T_{\max}$ occurs at the mean position (lowest point) and is given by:$T_{\max} = m g + \frac{m v^2}{l} = m g + \frac{m(2 g l(1 - \cos 	heta))}{l} = m g + 2 m g(1 - \cos 	heta) = m g(3 - 2 \cos 	heta)$The minimum tension $T_{\min}$ occurs at the extreme position where the velocity is zero:$T_{\min} = m g \cos 	heta$Given that $T_{\max} = 4 T_{\min}$:$m g(3 - 2 \cos 	heta) = 4 m g \cos 	heta$$3 - 2 \cos 	heta = 4 \cos 	heta$$3 = 6 \cos 	heta$$\cos 	heta = \frac{1}{2}$$	heta = 60^{\circ}$

The maximum value attained by the tension in the string of a swinging pendulum is four times the minimum value it attains. There is no slack in the string. The angular amplitude of the pendulum is (in $^{\circ}$)

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