Question

A ring of radius $R$ rolls without sliding with a constant velocity. If the radius of curvature of the path followed by any particle of the ring at the highest point of its path is $xR$. Find $x$.

Answer 1

$v_A=0$ (no slipping)

$⟹u=Rw$

Thus $v_B=u+Rw=2u$

Radius of curvature of point B, $R^{\prime }=\frac{(2u{)}^2}{a_c}$ where $a_c=\frac{u^2}{R}$

$⟹R^{\prime }=4R$