JEE Main & Advanced Physics Vectors Question Bank Fundamentals of Vectors

  • question_answer 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                                                                    [CBSE PMT 1995]

    A)            Parallel to the position vector

    B)            Perpendicular to the position vector

    C)            Directed towards the origin

    D)            Directed away from the origin

    Correct Answer: B

    Solution :

                 \[\vec{r}=(a\cos \omega \,t)\hat{i}+(a\sin \omega \,t)\hat{j}\]                    \[\vec{v}=\frac{d\vec{r}}{dt}=-a\omega \sin \omega \,t\,\hat{i}+a\omega \cos \omega \,t\,\hat{j}\]            As \[\vec{r}.\vec{v}=0\] therefore velocity of the particle is perpendicular to the position vector.


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