For a particle in a uniform circular motion, the acceleration $\overrightarrow{\text{a}}$ at a point $\mathrm{P}\left(\mathrm{R}, \mathrm{\theta }\right)$ on the circle of radius $\mathrm{R}$ is (here $\mathrm{\theta }$ is measured from the $\mathrm{y}$-axis)

• A

  $\frac{{\text{v}}^2}{\text{R}}\widehat{\text{i}}+\frac{{\text{v}}^2}{\text{R}}\widehat{\text{j}}$
• B

  $-\frac{{\text{v}}^2}{\text{R}}\text{cos }\mathrm{\theta }\widehat{\text{i}}+\frac{{\text{v}}^2}{\text{R}}\text{sin }\mathrm{\theta }\widehat{\text{j}}$
• Correct answer
  C

  $-\frac{{\text{v}}^2}{\text{R}}\text{sin }\mathrm{\theta }\widehat{\text{i}}-\frac{{\text{v}}^2}{\text{R}}\text{cos }\mathrm{\theta }\widehat{\text{j}}$
• D

  $-\frac{{\text{v}}^2}{\text{R}}\text{cos }\mathrm{\theta }\widehat{\text{i}}-\frac{{\text{v}}^2}{\text{R}}\text{sin }\mathrm{\theta }\widehat{\text{j}}$

Solution

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Hence, the correct answer is option: 'C'.