Question:
Find the angle in radian though 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
Solution:
We know that in a circle of radius $r$ unit, if an $\operatorname{arc}$ of length $/$ unit subtends an angle $\theta$ radian at the centre, then $\theta=\frac{l}{r}$.
It is given that $r=75 \mathrm{~cm}$
(i) Here, $I=10 \mathrm{~cm}$
$\theta=\frac{10}{75}$ radian $=\frac{2}{15}$ radian
(ii) Here, $I=15 \mathrm{~cm}$
$\theta=\frac{15}{75}$ radian $=\frac{1}{5}$ radian
(iii) Here, $I=21 \mathrm{~cm}$
$\theta=\frac{21}{75}$ radian $=\frac{7}{25}$ radian