question_answer

For a particle describing circular motion, the position is \[(r,\,\theta )\] then unit vector in radial direction can be given as

A)  \[{{e}_{r}}=\cos \theta \,\hat{i}+\sin \theta \hat{j}\]

B)  \[{{e}_{r}}=\tan \theta \,\hat{i}+\cot \theta \hat{j}\]

C)  \[{{e}_{r}}=-\cos \theta \,\hat{i}-\sin \theta \hat{j}\]

D)  \[{{e}_{r}}=(\sin \theta +\cos \theta )\hat{j}\]

E)  \[{{e}_{r}}=\cos \theta \hat{j}\]

Correct Answer: A

Solution :

                Consider the diagram given below From the figure \[\mathbf{PA}=\hat{i}\,PA\,\,\cos \theta +\hat{j}\,PA\,\,\sin \theta \] \[\frac{\mathbf{PA}}{PA}=\hat{i}\,\cos \theta +\hat{j}\,\,\sin \theta \]