A wheel of radius $2 \mathrm{~cm}$ is at rest on the horizontal surface. A point $\mathrm{P}$ on circumference of the wheel is in contact with the horizontal surface. When the wheel rolls without slipping on the surface, the displacement of point P after half rotation of wheel is

• A

  $2\left(\pi^{2}+2\right)^{\frac{1}{2}} \mathrm{~cm}$
• B

  $\left(\pi^{2}+2\right)^{\frac{1}{2}} \mathrm{~cm}$
• C

  $\left(\pi^{2}+4\right)^{\frac{1}{2}} \mathrm{~cm}$
• Correct answer
  D

  $2\left(\pi^{2}+4\right)^{\frac{1}{2}} \mathrm{~cm}$

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