Question

A ring of radius $R$ rolls without sliding with a constant velocity. The radius of curvature of the path followed by any particle of the ring at the highest point of its path will be

• A. $R$
• B. $2R$
• C. $4R$
• D. none of these

Answer 1

The correct option is C $4R$

$v_A=0$ (no slipping)

Thus $u=Rw$

$v_B=u+Rw=2u$

Radius of curvature of path followed by highest point, $R^{\prime }=\frac{(v_B{)}^2}{a_c}=\frac{4u^2}{\frac{u^2}{R}}$

$R^{\prime }=4R$