Question

A body moves over one-fourth of a circular arc in a circle of radius $r$. The magnitude of distance travelled and displacement will be respectively

• A. $\frac{\pi r}{2},r\sqrt{2}$
• B. $\frac{\pi r}{4},r$
• C. $\pi r,\frac{r}{\sqrt{2}}$
• D. $\pi r,r$

Answer 1

The correct option is A $\frac{\pi r}{2},r\sqrt{2}$



Let particle starts from A, its position vector $\overrightarrow{r_{OA}}=r\hat{i}$
After one quarter, positon vector $\overrightarrow{r_{OB}}=r\hat{j}$
So, displacement $=r\hat{j}-r\hat{i}$
Magnitude of displacement $=\sqrt{r^2+r^2}=r\sqrt{2}.$
And distance = One fourth of circumference $=\frac{2\pi r}{4}=\frac{\pi r}{2}$