Question

A car is moving on a circular level road of the radius of curvature $300 \, m$ . If the coefficient of friction is $0.3$ and acceleration due to gravity is $10 \, m \, s^{- 2}$ , the maximum speed the car can have is (in $km$ $h^{- 1}$ )

• A. $30kmh^{- 1}$
• B. $81kmh^{- 1}$
• C. $108kmh^{- 1}$
• D. $162kmh^{- 1}$

Answer 1

Answer: (C)

$r=300m$
$\mu = 0 \text{.} 3$
$\text{g}=10\text{m s}^{- 2}$
$\text{v}_{\text{max}} = \sqrt{\mu \text{rg}}$
$f_{s}\leq f_{s \left(\right. m a x \left.\right)}$
$\frac{m v^{2}}{r}\leq \mu mg$
$v^{2}\leq \mu rg$
$v\leq \sqrt{\mu r g}$
$v_{m a x}=\sqrt{\mu r g}$

$= \sqrt{\left(0 \text{.} 3\right) \left(3 0 0\right) \left(1 0\right)}$
$=30\text{m s}^{- 1}$
$=108kmh^{- 1}$