question_answer

A body covers an arc of a circle of radius 'r', subtending an angle of \[{{12}^{o}}\] at the centre of the circle. What is the magnitude of the displacement of the body? [Hint: Any line passing through the centre of the circle bisects the chord of the circle]

Answer:

Initial position = X Final position = Y Magnitude of displacement \[XY=?\] From figure,\[XY=XZ+ZY=2XZ\,\,or\,\,\,2ZY\] (according to hint given) Consider \[\Delta OZX,\,\,\sin 60{}^\circ \,=\frac{XZ}{r}XZ=r\sin 60{}^\circ \] \[=\frac{r\sqrt{3}}{2}\] \[\therefore XY=2XY=2\times \frac{r\sqrt{3}}{2}=\sqrt{3}r\]