A wheel of radius $2 \mathrm{~cm}$ is at rest on the horizontal surface. A point $\mathrm{P}$ on…

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

Solution

After half the rotation. the horizontal distance travelled by point P will be half the circumference of the wheel i.e. πR and the vertical distance will be 2R.

Asked in: MHT CET 2020 (12 Oct Shift 2)

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