Question

The displacement of the point of the wheel initially in contact with the ground, when the wheel roles forward half a revolution will be (radius of the wheel is R)

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

Answer 1

Answer: (B)

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

Answer 2

Horizontal distance covered by the wheel in half revolution

= πR

So the displacement of the point which was initially in contact with a ground = $\sqrt{(\pi R)^{2} + (2R)^{2}}$

$= R\sqrt{\pi^{2} + 4}.$