Question

If a given point $P$ is in contact with ground initially and wheel of radius $R$ is in pure rolling, then the displacement of point $P$ when point $P$ reaches topmost point of the sphere for the first time will be

• A. $\pi R$
• B. $2 \pi R$
• C. $\left(\sqrt{\left(\pi \right)^{2} + 1}\right) R$
• D. $\left(\sqrt{\left(\pi \right)^{2} + 4}\right) R$

Answer 1

Answer: (D)

The length of the horizontal path of the wheel when the point $P$ reaches the topmost point $=\pi R$

As shown in the figure, the displacement of the point $P$ will be
$d=\sqrt{\left(\right. \pi R \left(\left.\right)^{2} + \left(\right. 2 R \left(\left.\right)^{2}}=\sqrt{\left(\pi \right)^{2} + 4\right)}R$