question_answer

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

A)  \[2\text{ }r\text{ }sin(\theta /2)\]     

B)  \[2\text{ }r\text{ cos}(\theta /2)\]

C)  \[2\text{ }r\text{ tan}(\theta /2)\]     

D)  \[2\text{ }r\text{ cot}(\theta /2)\]

Correct Answer: A

Solution :

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