question_answer

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

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

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

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

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

Correct Answer: A

Solution :

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