A pendulum swings through an angle of 30° and describes an arc 8.8 cm in length.
Question:

A pendulum swings through an angle of 30° and describes an arc 8.8 cm in length. Find the length of the pendulum.

Solution:

Given:
Length of the arc = 8.8 cm
And,

$\theta=30^{\circ}$

Now,

Length of the $\operatorname{arc}=\frac{2 \pi \mathrm{r} \theta}{360}$

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

$\Rightarrow r=\frac{8.8 \times 360 \times 7}{44 \times 30}$

$\Rightarrow r=16.8 \mathrm{~cm}$

∴ Length of the pendulum = 16.8 cm

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