A particle of mass $\mathrm{m}$ is moving along a circle of radius $\mathrm{R}$ such that its tangential acceleration $\left(a_t\right)$ varies with distance covered $\left(x\right)$ as ${\mathrm{a}}_{\mathrm{t}}={\mathrm{\alpha x}}^2$, where $\alpha$ is a constant. The kinetic energy $\left(K\right)$ of the particle varies with the distance as $\mathrm{K}=\beta x^c$, where $\beta$ and $\mathrm{c}$ are constants. The values of $\beta$ and $\mathrm{c}$ are

• Correct answer
  A

  $\beta =\frac{m\alpha }{3};c=3$
• B

  $\beta =\frac{m\alpha }{4};c=4$
• C

  $\beta =\frac{m\alpha }{2};c=4$
• D

  $\beta =\frac{m\alpha }{2};c=3$

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