Physics - NLM Question with Solution | TestHub

The maximum safe speed on a curved road with zero banking angle is given by $v=\sqrt{\mu rg}$, where $\mu$ is the coefficient of friction, $r$ is the radius of the curve, and $g$ is the acceleration due to gravity.

For the dry road, the maximum safe speed is $v$, so the coefficient of friction ${\mu }_d$ is:

${\mu }_d=\frac{v^2}{rg}$

After heavy rain, the maximum safe speed is reduced by $60\%$. The new maximum safe speed $v^{\prime }$ on the wet road is:

$v^{\prime }=v-0.60v=0.40v$

The coefficient of friction for the wet road ${\mu }_w$ is:

${\mu }_w=\frac{v^{\prime 2}}{rg}=\frac{(0.40v{)}^2}{rg}=\frac{0.16v^2}{rg}$

The ratio of the coefficient of friction for the dry road to that of the wet road is:

$\frac{{\mu }_d}{{\mu }_w}=\frac{\frac{v^2}{rg}}{\frac{0.16v^2}{rg}}$

$\frac{{\mu }_d}{{\mu }_w}=\frac{1}{0.16}=\frac{100}{16}=\frac{25}{4}$