Question

A particle is moving in a circular path of radius r. The magnitude of displacement of the particle after covering $\frac{3}{4}th$ of the circle is

• A. 2r
• B. $\sqrt{2}r$
• C. $\frac{r}{2}$
• D. $\frac{3}{4}r$

Answer 1

The correct option is B $\sqrt{2}r$

Displacement is the shortest distance between two points. If the particle starts from point A, and after covering $\frac{3}{4}th$ of the circle, it reaches point B, then the displacement is given by AB.

In ΔAOB, using Pythagoras Theorem:
$(AB{)}^2=(BO{)}^2+(AO{)}^2$
$\Rightarrow (AB{)}^2=r^2+r^2$
$\Rightarrow (AB{)}^2=2r^2$
$\Rightarrow AB=\sqrt{2}r$
∴ Displacement, $AB=\sqrt{2}r$
Hence, the correct answer is option (b).