Question

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

• A. $2\text{r}\sin \left(\frac{\theta }{2}\right)$
• B. $2\text{r}\cos \left(\frac{\theta }{2}\right)$
• C. $2\text{r}\tan \left(\frac{\theta }{2}\right)$
• D. $2\text{r}\cot \left(\frac{\theta }{2}\right)$

Answer 1

The correct option is A $2\text{r}\sin \left(\frac{\theta }{2}\right)$



As shown in the figure for angular displacement $\theta$, the linear displacement $AB$ is equal to $2r\sin \left(\frac{\theta }{2}\right)$.