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Physics · PYQ NEET UG 2016(1)
हिन्दीA particle moves so that its position vector is given by \( \vec{r} = \cos\omega t\,\hat{x} + \sin\omega t\,\hat{y} \), where \( \omega \) is a constant. Which of the following is true?
Correct answer · Option B
Velocity is perpendicular to \( \vec{r} \) and acceleration is directed towards the origin.
Explanation
Velocity vector \( \vec{v} = \frac{d\vec{r}}{dt} = -\omega\sin\omega t\,\hat{x} + \omega\cos\omega t\,\hat{y} \). Dot product \( \vec{v} \cdot \vec{r} = 0 \), so velocity is perpendicular to \( \vec{r} \). Acceleration \( \vec{a} = -\omega^2 \vec{r} \), which is directed towards the origin.
