Question

The coefficient of friction between the tyres and the road is 0.25. The maximum speed with which car can be driven round a curve of radius 40 m without skidding is (assume g = 10 $ms^{- 2}$)

• A. 40 $ms^{-1}$
• B. 20 $ms^{-1}$
• C. 15 $ms^{-1}$
• D. 10 $ms^{-1}$

Answer 1

Answer: (D)

For turning around a curve, centripetal force is provided by friction, so
$\frac{m\nu^2}{r} < f$
$\frac{m\nu^2}{r} < \mu mg$
$\Rightarrow $ $\nu < \sqrt{\mu gr}$
= $\nu_{max} = \sqrt{\mu gr}$
Substituting , $\mu $ = 0.25,r = 40 m g = 10 $ms^{-2}$ , we get
$v_{max} = 10 \, ms^{-1}$