question_answer

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

A) \[2r\sin \left( \frac{\theta }{2} \right)\] 

B) \[2r\cos \left( \frac{\theta }{2} \right)\]

C) \[2r\tan \left( \frac{\theta }{2} \right)\]                

D) \[2r\cot \left( \frac{\theta }{2} \right)\]

Correct Answer: A

Solution :

\[\Delta r={{r}_{2}}-{{r}_{1}}\] Where, \[{{r}_{2}}={{r}_{1}}=r\] Hence \[\Delta r=\sqrt{r_{1}^{2}+r_{2}^{2}-2{{r}_{1}}{{r}_{2}}\cos \theta }\] \[=2r\sin \frac{\theta }{2}\]