Question

A particle is moving on a circular path of radius $r$ with uniform speed $v$. What is the displacement of the particle after it has described an angle of $60^?$?

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

Answer 1

Answer: (C)

$r$

Answer 2

According to cosine formula $cos\,60^{?}=\frac{r^{2}+r^{2}-x^{2}}{2r^{2}}$ $2r^{2}cos60^{?}=2r^{2}-x^{2}$ $x^{2}=2r^{2}-2r^{2}cos60^{?}$ $=2r^{2}\left[2sin^{2}\,30^{?}\right]=r^{2}$ $\therefore x=r$ Displacement $AB = x = r$