Question

A particle moves through angular displacement $ \theta $ on a circular path of radius $r$. The linear displacement will be :

• A. $ 2r \sin(\theta /2) $
• B. $ 2r\,\cos(\theta /2) $
• C. $ 2r\,\ tan(\theta /2) $
• D. $ 2r\,\cot(\theta /2) $

Answer 1

Answer: (A)

$\Delta \vec{ r }=\vec{ r }_{2}-\vec{ r }_{1}$,
where $r_{2}=r_{1}=r$

Hence, $\Delta r=\sqrt{r_{2}^{2}+r_{1}^{2}-2 r_{2} r_{1} \cos \theta}$
$=2 r \sin \frac{\theta}{2}$