Question

A body is in circular motion of radius pi M. Its distance after rotating an angle of 30 ° is

Answer 1

In the given question, we are given that the radius of circular path is $\pi \ m$.

After covering an angle of $30 ^\circ$, we have to find the distance covered.

Please refer to the attached figure in this answer:

The circular path mentioned in the form of red arc, is the length of arc to be calculated.

As per the formula of length of arc:

$\theta = \dfrac{l}{r}$

where $\theta$ is the angle made by the arc on center of circle,

$r$ is radius of circular path and  

$l$ is the length of arc .

Here, we are given the following:

$r = \pi\ m$

$\theta = 30 ^\circ$

We know that $\pi\text{ radians} = 180^\circ$

$\Rightarrow \theta = \dfrac{\pi}{6}$

$\Rightarrow \text{Distance covered} = \pi \times {\dfrac{\pi}{6}}$

$\Rightarrow \dfrac{\pi^{2}}{6}$

So, the distance covered by the body in circular motion after covering an angle of $30 ^\circ$ is $\dfrac{\pi^{2}}{6}\ m.$.