For a pacticle in uniform circular motion,

Question:

For a pacticle in uniform circular motion, the acceleration $\vec{a}$ at a point $P(R, \theta)$ on the circle of radius $R$ is (Here $\theta$ is measured from the $x$-axis).

  1. $\frac{v^{2}}{R} \hat{i}+\frac{v^{2}}{R} \hat{j}$

  2. $-\frac{\mathrm{v}^{2}}{\mathrm{R}} \cos \theta \hat{\mathrm{i}}+\frac{\mathrm{v}^{2}}{\mathrm{R}} \sin \theta \hat{\mathrm{j}}$

  3. $-\frac{v^{2}}{R} \sin \theta \hat{i}+\frac{v^{2}}{R} \cos \theta \hat{j}$

  4. $-\frac{\mathrm{v}^{2}}{\mathrm{R}} \cos \theta \hat{\mathrm{i}}-\frac{\mathrm{v}^{2}}{\mathrm{R}} \sin \theta \hat{\mathrm{j}}$


Correct Option: , 4

Solution:

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