Find the angle in radian though which a pendulum swings if its length

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

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