A particle moves so that its position vector is given by r = cos ω t x + sin ω t y, where ω is a constant. Which of the following is true? (a) Velocity is perpendicular to r and acceleration is directed towards the origin. (b) Velocity is perpendicular to r and acceleration is directed away from the origin. (c) Velocity and acceleration both are perpendicular to r (d) Velocity and acceleration both are parallel to r

Answer: (a). v = -ωsin ω t x + ωcos ω t y, and v· r = 0, so v ⊥ r a = (d v)/(dt) = -ω² r, so a points towards the origin So the answer is (a).

A particle moves so that its position vector is given by r = cos ω t… | NEET 2016 (Phase 1)

Q15NEET 2016 · PHASE 1Medium

Motion in a Plane (2-D Kinematics)

A 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?

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Answer: (a)

$\vec v = -\omega\sin\omega t\,\hat x + \omega\cos\omega t\,\hat y$ , and $\vec v\cdot\vec r = 0$ , so $\vec v \perp \vec r$
$\vec a = \frac{d\vec v}{dt} = -\omega^2\vec r$ , so $\vec a$ points towards the origin
So the answer is (a).

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