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) We have,

OA = length of pendulum = 75 cm

= 0.75 m

AB = arc AB = 10 cm

= 0.1 m

Also,

$\theta =\frac{\text{arc}}{\text{radius}}$ . . .(i)

$\theta =\frac{0.1}{0.75}={\left(\frac{2}{15}\right)}^c$

$\theta =\frac{2}{15}\text{radian}$

(ii) OA = 75 cm = 0.75 cm

AB = 15 cm = 0.15 m

From (A)

$\theta =\frac{0.15}{0.75}=\frac{1}{5}\text{radian}$

$\theta =\frac{1}{5}\text{radian}$

(iii) OA = 75 cm 0.75 m

AB = 21 cm = 0.21 m

From (A)

$\theta =\frac{0.21}{0.75}=\frac{7}{25}$

$\theta =\frac{7}{25}\text{radian}$