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

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