Question

When the road is dry and the coefficient of friction is $\mu$, the maximum speed of a car in a circular path is $10\mspace{6mu} m/s$. If the road becomes wet and $\mu^{'} = \frac{\mu}{2}$, what is the maximum speed permitted

• A. $5\mspace{6mu} m/s$
• B. $10\mspace{6mu} m/s$
• C. $10\sqrt{2}\mspace{6mu} m/s$
• D. $5\sqrt{2}\mspace{6mu} m/s$

Answer 1

Answer: (D)

$5\sqrt{2}\mspace{6mu} m/s$

Answer 2

$v \propto \sqrt{\mu}$ ⇒ $\frac{v_{2}}{v_{1}} = \sqrt{\frac{\mu_{2}}{\mu_{1}}} = \sqrt{\frac{\mu/2}{\mu}} = \frac{1}{\sqrt{2}}$

⇒ $v_{2} = \frac{1}{\sqrt{2}}v_{1}$ ⇒ $v_{2} = \frac{10}{\sqrt{2}} = 5\sqrt{2}m/s$