For a particle in uniform circular motion, the acceleration a at any point P(R, θ) on the circular path of radius R is (when θ is measured from the positive x-axis and v is uniform speed): (a) -v²/Rsin θ i + v²/Rcos θ j (b) -v²/Rcos θ i + v²/Rsin θ j (c) -v²/Rcos θ i - v²/Rsin θ j (d) -v²/Ri + v²/Rj

Answer: (c). In UCM the acceleration has magnitude v²/R and points from P towards the centre. Position unit vector of P is cos θ i + sin θ j; the acceleration is opposite to it. a = -v²/Rcos θ i - v²/Rsin θ j So the answer is (c).

For a particle in uniform circular motion, the acceleration a at any… | JEE Main 2022 (25 Jun, Shift 2)

Q27JEE Main 2022 · 25 JUN · SHIFT 2Medium

Centripetal Acceleration & Force

For a particle in uniform circular motion, the acceleration $\vec{a}$ at any point P(R, $\theta$ ) on the circular path of radius R is (when $\theta$ is measured from the positive x-axis and v is uniform speed):

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Answer: (c)

In UCM the acceleration has magnitude $\frac{v^2}{R}$ and points from P towards the centre.
Position unit vector of P is $\cos\theta\,\hat{i} + \sin\theta\,\hat{j}$ ; the acceleration is opposite to it.
$\vec a = -\frac{v^2}{R}\cos\theta\,\hat{i} - \frac{v^2}{R}\sin\theta\,\hat{j}$
So the answer is (c).

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