Question

A pendulum swings through an angle of ${30}^{\circ }$ and describes an arc 8.8 cm in length. Find the length of pendulum in cm.

Answer 1

Let $r$ be the length of the pendulum.

Given: Length of arc = 8.8 cm.
$\angle AOB={30}^{\circ }$

Length of an arc of a sector of an angle $\theta =\frac{\theta }{360}\times 2\pi r$

$\Rightarrow 8.8=\frac{30°}{360°}\times 2\times \frac{22}{7}\times r$

$r=\frac{8.8\times 21}{11}=16.8cm$ (2 mark)