Question

The minimum velocity in ($m{s}^{-1}$) with which a car driver must traverse a flat curve of radius $150m$ and coefficient of friction $0.6$ to avoid skidding is ?

• A. $60m{s}^{-1}$
• B. $30m{s}^{-1}$
• C. $15m{s}^{-1}$
• D. $25m{s}^{-1}$

Answer 1

The correct option is B

$30m{s}^{-1}$

Step 1: Given data

The radius of the curve, $r=150m$

Coefficient of friction, $\mu =0.6$

We know, that acceleration due to gravity, $g=10m{s}^{-2}$

Step 2: Formula used

The condition to avoid skidding is: $\frac{m{v}^2}{r}=\mu N=\mu mg$

$\Rightarrow \frac{v^2}{r}=\mu g$.

$v\to$ minimum speed to avoid skidding

$m\to$mass of the body

Step 3: Substituting the values

$\frac{v^2}{r}=\mu g$

$$\begin{gathered} \Rightarrow v^2=\mu rg \\ \Rightarrow v^2=0.6\times 150\times 10m^2{s}^{-2} \\ \Rightarrow v^2=900 \\ \Rightarrow v=30m{s}^{-1} \end{gathered}$$

The minimum velocity in which a car driver must traverse a flat curve of radius $150m$ and coefficient of friction $0.6$ to avoid skidding is $30m{s}^{-1}$.