Question

Find the angle in radians through which a pendulum swings if its length is 75 cm and the tip describes an arc of length (i) 10 cm (ii) 15 cm (iii) 21 cm.

Answer 1

We know:
Radius = 75 cm

(i)
Length of the arc = 10 cm
Now,
$$\begin{gathered} \mathrm{\theta }=\frac{\mathrm{Arc}}{\mathrm{Radius}} \\ =\frac{10}{75} \\ =\frac{2}{15}\mathrm{radian} \end{gathered}$$

(ii)
Length of the arc = 15 cm
Now,
$$\begin{gathered} \mathrm{\theta }=\frac{\mathrm{Arc}}{\mathrm{Radius}} \\ =\frac{15}{75} \\ =\frac{1}{5}\mathrm{radian} \end{gathered}$$

(iii)
Length of the arc = 21 cm
Now,
$$\begin{gathered} \mathrm{\theta }=\frac{\mathrm{Arc}}{\mathrm{Radius}} \\ =\frac{21}{75} \\ =\frac{7}{25}\mathrm{radian} \end{gathered}$$