Question

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

• A. $\frac{R}{\sqrt{{\pi }^2+1}}$
• B. $R\sqrt{{\pi }^2+4}$
• C. $2\pi R$
• D. $\pi R$

Answer 1

The correct option is B $R\sqrt{{\pi }^2+4}$


Horizontal distance covered by the wheel in half revolution $=\pi R$
So, displacement of the point which was initially in contact with the ground $=\sqrt{(\pi R{)}^2+(2R{)}^2}=R\sqrt{{\pi }^2+4}$