Question

A person covers $\frac{1}{3}rd$ of a circle of radius $10\text{m}$. Calculate angular displacement in radians & degrees.

• A. $\frac{\pi }{3}\text{rad},{60}^{\circ }$
• B. $\pi \text{rad},{180}^{\circ }$
• C. $\frac{\pi }{4}\text{rad}.{45}^{\circ }$
• D. $\frac{2\pi }{3}\text{rad},{120}^{\circ }$

Answer 1

The correct option is D $\frac{2\pi }{3}\text{rad},{120}^{\circ }$


Angular displacement in complete circle $=2\pi$
So, Angular displacment in one - third of a circle = $2\pi \times \frac{1}{3}$
$=\frac{2\pi }{3}\text{rad}$
Angular displacement $=\frac{2\pi }{3}\times \frac{360}{2\pi }$
in degree $={120}^{\circ }$