In a continuous printing process, paper roll is wrapped on a cylindrical core which is free to rotate about a fixed horizontal axis. The paper is drawn into the process at a constant speed $v$, as shown in the figure. If $r$ is the radius of paper on the roll at any given time and $b$ is the thickness of the paper, then the angular acceleration of the roll at this instant is

• A

  $\frac{v^{2}b}{2{\pi }^2{r}^3}$
• B

  zero because $v$ is constant

• Correct answer
  C

  $\frac{v^{2}b}{2\pi r^3}$
• D

  cannot be calculated from given information

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