A pendulum swings through an angle of 30º and describes an arc 8.8 cm in length. Find the length of the pendulum. (Use π=22/7)

Question

A pendulum swings through an angle of 30º and describes an arc 8.8 cm in length. Find the length of the pendulum. \(\big(\text{Use}\,π= \frac{22}{7}\big)\)

Answer 1

Given fig. depicts the pendulum

Here θ = 30º, arc length = l = 8.8, length of the pendulum = radius = r

∵ l = \(\frac{\theta}{360^0}\) × 2πr

∴ 8.8 = \(\frac{30}{360}\) × 2 × \(\frac{22}{7}\) × r 

⇒ r = \(\frac{8.8 \times 6\times 22}{22}\) 

= 16.8 cm.