Question

Given that $P$ is a point on a wheel rolling on a horizontal ground. The radius of the wheel is $R$. Initially if the point $P$ is in contact with the ground, the wheel rolls through half revolution. What is the displacement of point $P$?

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

Answer 1

Answer: (B)

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

Displacement of $P\Rightarrow \pi R\overrightarrow{i}+2R\overrightarrow{j}$
Displacement of $P\Rightarrow \sqrt{{\left(2R\right)}^2+{\left(\pi R\right)}^2}=R\sqrt{4+{\pi }^2}$