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

Answer 1

We know that in a circle of radius r unit, if an arc of length / unit subtends an angle θ radian at the centre, then .

$θ=\frac{i}{r}$

It is given that r = 75 cm

(i) Here, l = 10 cm

$θ=\frac{10}{75}\,radian=\frac{2}{15}\,radian$

(ii) Here, l = 15 cm

$θ=\frac{15}{75}\,radian=\frac{1}{5}\,radian$

(iii) Here, l = 21 cm

$θ=\frac{21}{75}\,radian=\frac{7}{25}\,radian$