Question

A motorcyclist of mass $m$ is to negotiate a curve of radius $r$ with a speed $v.$ The minimum value of the coefficient of friction so that this negotiation may take place safely is

• A. $v^{2}rg$
• B. $\frac{v^2}{gr}$
• C. $\frac{gr}{v^2}$
• D. $\frac{g}{v^{2}r}$

Answer 1

The correct option is B

$\frac{v^2}{gr}$

The frictional force is balanced by the centrifugal force

$f=\frac{m{v}^2}{r}$

Where, $f$ is the force

$m$ is the mass

$v$ is the velocity

$r$ is the radius

We also know, $f=\mu N=\mu mg$

Where, $\mu$ is the coefficient of friction

$g$ is acceleration due to gravity

Now by equating both equations we get,

$$\begin{gathered} \frac{m{v}^2}{r}=\mu mg \\ \mu =\frac{v^2}{gr} \end{gathered}$$

Hence, the correct option is (B).