Question

What the road is dry and the coefficient of friction is $\mu$, the maximum speed of a car in a circular path is $10m/s$, If the road becomes wet and coefficient of friction is${\mu }^{\prime }=\mu /2$. What is the maximum speed permitted?

• A. $5$ $m/s$
• B. $10$ $m/s$
• C. $10\sqrt{2}$ $m/s$
• D. $5\sqrt{2}$ $m/s$

Answer 1

The correct option is D $5\sqrt{2}$ $m/s$

Friction force resist the car not slip while moving in circular path

so eq is

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

while road is dry the coefficient of friction is $\mu$

$f=\mu N$

$N=Mg$

$\Rightarrow f=\mu Mg=\frac{M{v}^2}{r}$

$\Rightarrow v\propto \sqrt{\mu }=k\sqrt{\mu }$ ---eq1

k is proportionally constant

when road is wet thancofficient of friction is $\frac{\mu }{2}$

$v_1=k\sqrt{\frac{\mu }{2}}$.. eq2

by eq1 and eq2

$\frac{v_1}{v}=\frac{\sqrt{\frac{\mu }{2}}}{\sqrt{\mu }}$

$v_1=v\times \frac{1}{\sqrt{2}}=5\sqrt{2}m/s$

Hence the correct option is D