Question

A particle moves on a circular arc of radius $r$, the distance covered by particle when it travels from $A$ to $B$ on the arc subtending an angle ${60}^{\circ }$ at centre of circular path.

• A. $\frac{2\pi r}{9}$
• B. $\frac{2\pi r}{6}$
• C. $\frac{3\pi r}{4}$
• D. $\frac{2\pi r}{8}$

Answer 1

The correct option is B $\frac{2\pi r}{6}$

In this case the distance travelled by particle will be equal to perimeter of arc or length of arc.

Distance travelled will be,
$S=2\pi r\left(\frac{\theta }{{360}^{\circ }}\right)$
Here $\theta ={60}^{\circ }$
$\Rightarrow S=2\pi r\left(\frac{{60}^{\circ }}{{360}^{\circ }}\right)$
$\therefore S=\frac{2\pi r}{6}$
Hence we can see that distance travelled will be $\frac{1}{6}\text{th}$ of the total circumference of circular path.