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

Answer: (A)

$\frac{\pi r}{2},r\sqrt{2}$

Here a body moves over one fourth of a circular arc in a circle of radius $r$

We have,

Perimeter of a circle $=2\pi r$

The magnitude of the distance travelled by the body is equal to the perimeter

of the one fourth of the circular arc

Perimeter of one fourth of the circular arc $=\frac{2\pi r}{4}=\frac{\pi r}{2}$

Displacement is the minimum distance to the destination.

Here the displacement can be calculated by using pythagorous theorem.

Displacement $=\sqrt{r^2+r^2}=\sqrt{2r^2}=r\sqrt{2}$

So, the magnitude of distance travelled is $\frac{\pi r}{2}$ and the

dispacement is $r\sqrt{2}$