A ring is rolling without slipping on a plane surface as shown in figure. If speed of A is 4 m/s, speed of B is

If $\omega$ be its angular velocity and since O is the instantaneous centre of rotation, then ${\text{V}}_{\text{A}}\text{=ω×OA}$ and ${\text{V}}_{\text{B}}\text{=ω×OB}$

$\therefore \frac{{\mathrm{V}}_{\mathrm{B}}}{{\mathrm{V}}_{\mathrm{A}}}=\frac{\mathrm{\omega }\times \mathrm{OB}}{\mathrm{\omega }\times \mathrm{OA}}=\frac{\sqrt{2}\mathrm{R}}{2\mathrm{R}}\Rightarrow \frac{{\mathrm{V}}_{\mathrm{B}}}{\mathrm{V}}=\frac{1}{\sqrt{2}}\Rightarrow {\mathrm{V}}_{\mathrm{B}}=2\sqrt{2}\mathrm{m}/\mathrm{s}$