Question

A particle is moving uniformly in a circular path of radius $10m$. When it moves through a displacement $5m$, then the magnitude of the corresponding angular displacement will be:

• A. ${20}^o$
• B. ${30}^o$
• C. ${60}^0$
• D. ${90}^o$

Answer 1

The correct option is C ${60}^0$

In the figure, the angle AOB is equal to $\theta$.

The liner displacement corresponding to the angular displacement $\theta$ is AB.

We know AB = 5 m and r = 10 m

Let C be the mid point of AB. Hence the angle $COB$ is $\theta /2$.
Since OBC forms a right angle triangle, $BC=rsin\left(\frac{\theta }{2}\right)$

Hence $AB=2BC=2rsin\left(\frac{\theta }{2}\right)$

$\Rightarrow \theta =2\times si{n}^{-1}\left(\frac{AB}{2r}\right)$

$\Rightarrow \theta =2\times si{n}^{-1}\left(\frac{5}{2\times 5}\right)$

$\Rightarrow \theta =2\times {30}^{\circ }$

$\Rightarrow \theta ={60}^{\circ }$