Question

A car of mass m is moving on a level circular track of radius R. If u_s represents the static friction between the road and tyres of the car,the maximum speed of the car in circular motion is given by?

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{necessary}\mathrm{centripetal}\mathrm{force}\mathrm{required}\mathrm{for}\mathrm{circular}\mathrm{motion}\mathrm{is}\mathrm{provided}\mathrm{by} \\ \mathrm{frictional}\mathrm{force}: \\ \mathrm{frictional}\mathrm{force}=\mathrm{centripetal}\mathrm{force} \\ \mathrm{\mu mg}=\frac{{\mathrm{mv}}^2}{\mathrm{r}} \\ \mathrm{\mu g}=\frac{{\mathrm{v}}^2}{\mathrm{r}} \\ \mathrm{v}=\sqrt{\mathrm{\mu gr}} \\ =\sqrt{{\mathbf{\mu }}_{\mathbf{s}}\mathbf{gR}} \end{gathered}$$