Question

A wheel of radius 1 meter rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is

• A. $2\pi$
• B. $\sqrt{2}\pi$
• C. $\sqrt{{\pi }^2+4}$
• D. $\pi$

Answer 1

The correct option is C

$\sqrt{{\pi }^2+4}$

Horizontal distance covered by the wheel in half revolution = $\pi R$

So the displacement of the point which was initially in contact with ground = $A{A}^{{}^{\prime }}=\sqrt{(\pi R{)}^2+(2R{)}^2}$
=$R\sqrt{{\pi }^2+4}=\sqrt{{\pi }^2+4}$ (As R=1m)