Question

A circle of radius $r$ moves forward on the ground and completes a full revolution. Find the final position of the centre of the circle after the revolution.

• A. $0\hat{i}+r\hat{j}$
• B. $2\pi r\hat{i}+r\hat{j}$
• C. $\pi r^2\hat{i}+r\hat{j}$
• D. $r\hat{i}+2\pi r\hat{j}$

Answer 1

The correct option is B $2\pi r\hat{i}+r\hat{j}$

When a circle rolls and complete one revolution, then the point in contact with the ground also covers a distance of $2\pi r$.
Hence, distance covered by point $O$ in $\text{x}$ direction = $2\pi r$

$\therefore$ Position of point $O$ after one revolution = $2\pi r\hat{i}+r\hat{j}$

Hence, option $\text{(D)}$ is the correct answer.