A) parallel to position vector
B) perpendicular to position vector
C) directed towards the origin
D) directed away from the origin
Correct Answer: B
Solution :
Position vector, \[r=(a\cos \omega t)\,\hat{i}+(a\sin \omega t)\hat{j}\] Velocity \[v=\frac{dr}{dt}\] \[=\frac{d}{dt}[(a\cos \omega t)\hat{i}+(a\sin \omega t)\hat{j}]\] \[=(-a\sin \omega t)\hat{i}+(a\cos \omega t)\hat{j}\] \[v.r=[(-a\sin \omega t)\hat{i}+(a\cos \omega t)\hat{j}]\] \[[(a\cos \omega t)\hat{i}+(a\sin \omega t)\hat{j}]\] \[v.r=0\] i.e., velocity vector is perpendicular to position vector.
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