Find the angle in radians through which a pendulum swings if its length is \(75\) cm and the tip describes an arc of length \(15\) cm.
Solution:
We know:
\[ s=r\theta \]
Given:
\[ s=15 \text{ cm} \]
\[ r=75 \text{ cm} \]
Using,
\[ \theta=\frac{s}{r} \]
\[ \theta=\frac{15}{75} \]
\[ \theta=\frac{1}{5} \]
Therefore, the angle through which the pendulum swings is:
\[ \boxed{\frac{1}{5} \text{ radians}} \]