Two concentric circles have radii and

MATHEMATICS · Subjective · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

Two concentric circles have radii

r_{1}=10\,\text{cm}

and

r_{2}=15\,\text{cm}

. (i) Prove that for any common angular displacement

\theta

(in radians) subtended at the common centre, the ratio of the corresponding arc lengths

s_{1}

and

s_{2}

is equal to the ratio of their radii. (ii) When

\theta = 72^{\circ}

, calculate the individual arc lengths

s_{1}

and

s_{2}

and hence their difference. Give your answers in metres, taking

\pi = 22/7

. (iii) If the difference between the two arc lengths is measured to be

0.314\,\text{m}

, find the angular displacement

\theta

in degrees (use

\pi = 3.14