A point P consider at the contact point of a wheel on the ground which roll on the ground without slipping,…

A point P consider at the contact point of a wheel on the ground which roll on the ground without slipping, then the value of the displacement of point $\mathrm{P}$ when wheel completes half of the rotation (if radius of wheel is $1 \mathrm{~m}$ )is:
  1. $2 \mathrm{~m}$
  2. $\sqrt{\pi^2+4} \mathrm{~m}$
  3. $\pi \mathrm{m}$
  4. $\sqrt{\pi^2+2} \mathrm{~m}$

Solution

Displacement $P Q$ $\begin{aligned} & =\sqrt{(P M)^2+(Q M)^2} \\ & =\sqrt{(\pi R)^2+(2 R)^2} \\ & =\sqrt{\pi^2+4}\{\because R=1 \mathrm{~m}\} \end{aligned}$

Asked in: NEET 2002

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