# Find the angle in radians through which a pendulum swings if its length is 75 cm and the tip describes an arc of length

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.

Solution:

We know:

Radius = 75 cm

(i) Length of the arc = 10 cm

Now,

$\theta=\frac{\text { Radius }}{\text { Rade }}$

$=\frac{10}{75}$

$=\frac{2}{15} \operatorname{radian}$

(ii) Length of the arc = 15 cm

Now,

$\theta=\frac{\text { Arc }}{\text { Radius }}$

$=\frac{15}{75}$

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

(iii) Length of the arc = 21 cm

Now,

$\theta=\frac{\text { Arc }}{\text { Radius }}$

$=\frac{21}{75}$

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