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.

• A. 14.5
• B. 15.1
• C. 17.3
• D. 16.8

Answer 1

The correct option is D

16.8

Let r be the length of the pendulum

Length of arc = 8.8 cm

$\angle$AOB = 30 ${}^{\circ }$

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

Length of arc
$=\frac{\theta }{360}\times 2\pi r$

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

$r=\frac{8.8\times 21}{11}=16.8cm$