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

(i) Here, length of pendulum r = 75 cm

Length of arc l = 10 cm

We know that ${\theta }^C=\frac{l}{r}$

$\therefore \theta =\frac{10}{75}={\left(\frac{2}{15}\right)}^C$

(ii) Here, length of pendulum r = 75 cm

Length of arc l = 15 cm

We know that ${\theta }^C=\frac{l}{r}$

$\therefore \theta =\frac{15}{75}={\left(\frac{1}{5}\right)}^C$

(iii) Here, length of pendulum r = 75 cm

Length of arc l = 21 cm

We know that ${\theta }^C=\frac{l}{r}$

$\therefore \theta =\frac{21}{75}={\left(\frac{7}{25}\right)}^C$