Question 78

A pendulum of length 'l' swings through an angle of $$45^\circ$$ and describes an arc of length 15.4 cm. Find the value of 'l'.

Solution

length of pendulum is l

angle of swing $$\theta$$ = $$45^\circ$$

length of arc = 15.4

length of pendulum = radius

length of arc of circle = 2$$\pi$$r * $$\frac{\theta}{360}$$

15.4 = $$\frac{\theta}{360}$$ * 2 * $$\frac{22}{7}$$ * l

15.4 = $$\frac{1}{8}$$ * $$\frac{44}{7}$$ * l

15.4 = $$\frac{11}{14}$$ * l

l = 15.4 * $$\frac{14}{11}$$

l = 19.6

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