Question

On a dry road, the maximum permissible speed of a car in a circular path is $10m{s}^{-1}$ and speed is $5\sqrt{2}m{s}^{-1}$ on wet surface of the same road. If the coefficient of friction for dry road is $\mu$ , then that for the wet road is:

• A. $\frac{\mu }{2}$
• B. $\frac{\mu }{3}$
• C. $\frac{2\mu }{3}$
• D. $\frac{3\mu }{4}$

Answer 1

Answer: (A)

$\frac{\mu }{2}$

Required centripetal force is provided by the frictional force,therefore,

$\mu N=\frac{m{v}^2}{R}$
$N=mg$
$\mu mg=\frac{m{v}^2}{R}$

$\frac{{\mu }_{1}mg=\frac{m{v_1}^2}{R}}{{\mu }_{2}mg=\frac{m{v_2}^2}{R}}$

$\frac{{\mu }_1}{{\mu }_2}={\left(\frac{V_1}{V_2}\right)}^2$

$={\left(\frac{10}{5\sqrt{2}}\right)}^2$

${\mu }_2=\frac{{\mu }_1}{2}$
$\therefore {\mu }_2=\mu {/}_2$