Question

An engineer has designed a road with a curve of radius $12\text{m}$. The material of the road offers a maximum coefficient of friction of $0.3$. What should be the maximum permissible speed limit on this road?

• A. $7\text{m/s}$
• B. $8\text{m/s}$
• C. $6\text{m/s}$
• D. $5\text{m/s}$

Answer 1

The correct option is C $6\text{m/s}$

The velocity can be increased upto the limit where the friction provides the necessary centripetal force.
i.e$\frac{m{v}^2}{r}=f\le \mu mg$
$\Rightarrow v\le \sqrt{\mu rg}=\sqrt{0.3\times 12\times 10}$
$\Rightarrow v\le 6\text{m/s}$
or $v_{max}=6\text{m/s}$