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Question: A body moves over one fourth of a circular arc in a circle of radius r. The magnitude of distance tr...

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

πr2,r2\frac{\pi r}{2},r\sqrt{2}

B

πr4,r\frac{\pi r}{4},r

C

πr,r2\pi r,\frac{r}{\sqrt{2}}

D

πr,r\pi r,r

Answer

πr2,r2\frac{\pi r}{2},r\sqrt{2}

Explanation

Solution

Let particle start from A, its position vector r→OA=ri^{{\overrightarrow{r}}_{O}}_{A} = r\widehat{i}

After one quarter position vector r→OB=rj^.{\overrightarrow{r}}_{OB} = r\widehat{j}.

So displacement =rj^−ri^= r\widehat{j} - r\widehat{i}

Magnitude of displacement =r2.= r\sqrt{2}. and distance = one fourth of circumference =2πr4=πr2= \frac{2\pi r}{4} = \frac{\pi r}{2}