A disc is rolling without slipping on a surface. The radius of the disc is $R$. At $t=0$, the top most point on the disc is $\mathrm{A}$ as shown in figure. When the disc completes half of its rotation, the displacement of point $A$ from its initial position is

• Correct answer
  A

  $\mathrm{R} \sqrt{\left(\pi^2+4\right)}$
• B

  $\mathrm{R} \sqrt{\left(\pi^2+1\right)}$
• C

  $2 \mathrm{R}$
• D

  $2 \mathrm{R} \sqrt{\left(1+4 \pi^2\right)}$

Solution

(a) From figure,


Displacement,
$\mathrm{BA}=\sqrt{(2 \mathrm{R})^2+(\pi \mathrm{R})^2}=\mathrm{R} \sqrt{4+\pi^2}$

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