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

Answer 1

We know that in a circle of radius $r$ unit, if an arc of length $l$ unit subtends an angle $\theta$ radian at the centre, then $\theta =\frac{l}{r}$.
It is given that $r=75$ cm

(i) $l=10$ cm

$\therefore \theta =\frac{10}{75}=\frac{2}{15}$ radian

(ii) $l=15$ cm

$\therefore \theta =\frac{15}{75}=\frac{1}{5}$ radian

(iii) $l=21$ cm

$\therefore \theta =\frac{21}{75}=\frac{7}{25}$ radian