Question

The maximum speed with which a vehicle can take the safely circular turn on a horizontal flat rough road is (where symbols have their usual meanings).

• A. $\mu \sqrt{rg}$
• B. $\sqrt{\frac{rg}{\mu }}$
• C. $\sqrt{rg}$
• D. $\sqrt{rg\mu }$

Answer 1

The correct option is D $\sqrt{rg\mu }$

Turning on level road:

$N=mg$

$f\ge \frac{m{v}^2}{r}$ (so, that the vehicle may not slip)

$⟹\mu mg\ge \frac{m{v}^2}{r}$

$⟹V\le \sqrt{\mu rg}$

$⟹V_{max}=\sqrt{\mu rg}$