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3-2.Motion in Plane
medium
The position vector of a particle is $\vec r = (a\cos \omega t)\hat i + (a\sin \omega t)\hat j$. The velocity of the particle is
AParallel to the position vector
BPerpendicular to the position vector
CDirected towards the origin
DDirected away from the origin
(AIPMT-1995)
Solution
(b) $\vec r = (a\cos \omega \,t)\hat i + (a\sin \omega \,t)\hat j$
$\vec v = \frac{{d\vec r}}{{dt}} = – a\omega \sin \omega \,t\,\hat i + a\omega \cos \omega \,t\,\hat j$
As $\vec r.\vec v = 0$ therefore velocity of the particle is perpendicular to the position vector.
$\vec v = \frac{{d\vec r}}{{dt}} = – a\omega \sin \omega \,t\,\hat i + a\omega \cos \omega \,t\,\hat j$
As $\vec r.\vec v = 0$ therefore velocity of the particle is perpendicular to the position vector.
Standard 11
Physics
