Question

Find the angle in radian through which a pendulum swings if its length is $75$ cm and the tip describes an arc of length
$\left(A\right)10$ cm
$\left(B\right)15$ cm
$\left(C\right)21$ cm

Answer 1

$\left(A\right)$
Length of arc $\left(l\right)=10$ cm
Length of pendulum $\left(r\right)=75$ cm
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
$\theta =\frac{l}{r}$ radian
$\Rightarrow \theta =\frac{10}{75}$ radian $=\frac{2}{15}$ radian

$\left(B\right)$
Length of arc $\left(l\right)=15$ cm
Length of pendulum $\left(r\right)=75$ cm
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
$\theta =\frac{l}{r}$ radian
$\Rightarrow \theta =\frac{15}{75}$ radian $=\frac{1}{5}$ radian

$\left(C\right)$
Length of arc $\left(l\right)=21$ cm
Length of pendulum $\left(r\right)=75$ cm
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
$\theta =\frac{l}{r}$ radian
$\Rightarrow \theta =\frac{21}{75}$ radian $=\frac{7}{25}$ radian