Question

For a circle of radius $r=2m$, the angle subtended by an arc of length $\frac{\pi }{2}m$ will be

• A.
  $\pi \mathrm{radians}$
• B.
  $\frac{\pi }{2}\mathrm{radians}$
• C.
  $\frac{\pi }{4}\mathrm{radians}$
• D.
  $\frac{\pi }{8}\mathrm{radians}$

Answer 1

The correct option is C

$\frac{\pi }{4}\mathrm{radians}$
We know that the angle $\theta$ (in radian) subtended by an arc of length $l$ on a circle of radius $r$ is given by
$\theta =\frac{l}{r}$
Now, for the given question,
$\mathrm{radius}r=2m,\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{arc}\left(l\right)=\frac{\pi }{2}m$
Using,
$\theta =\frac{l}{r}=\frac{\pi }{2\times 2}=\frac{\pi }{4}\mathrm{radians}$
Hence, the option (c) is correct.