Question

A car round on unbanked curve of radius $92 \, m$ without skidding at a speed of $26 \, m \, s^{- 1}$ . The smallest possible coefficient of static friction between the tyres and the road is

• A. $0.75$
• B. $0.60$
• C. $0.45$
• D. $0.30$

Answer 1

Answer: (A)

$f_{s}\leq f_{s \left(max\right)}$
Centripetal force is equal to maximum static friction
$\frac{m v^{2}}{r}\leq \mu mg$
$\mu \geq \frac{v^{2}}{r g}$
$\mu _{min}=\frac{v^{2}}{r g}$
$\left(\mu \right)_{min}=\frac{\left(26\right)^{2}}{92 \times 9 . 8}$
$\mu _{min}=0.75$