Question

What will be the maximum speed of a car on a road-turn of radius $30 \, m$ if the coefficient of friction between the tyres and the road is $0.4?$ (Take $g=9.8 \, m \, s^{- 2}$ )

• A. $10.84ms^{- 1}$
• B. $9.84ms^{- 1}$
• C. $8.84ms^{- 1}$
• D. $6.84ms^{- 1}$

Answer 1

Answer: (A)

Given
$r = 30 \, m \, \, and \, \, \mu = 0.4.$
$v_{max} = \sqrt{\mu r g} = \sqrt{0.4 \times 30 \times 9.8} = 10.84 \, m \, s^{- 1}$
For a safe turn
$\frac{M v^{2}}{r}\leq \mu _{s} \, Mg \\ or \, v^{2}\leq \mu _{s} \, rg$
where $\mu _{s} \rightarrow $ coefficient of static friction