Question

A car turns a corner on a slippery road at a constant speed of $12m/s$. If the coefficient of friction is $0.4$, the minimum radius of the arc in meters in which the car turns is?

• A. $9$
• B. $18$
• C. $36$
• D. $72$

Answer 1

The correct option is C

$36$

Step 1: Given

Velocity of the car, $v=12m/s$

Coefficient of friction, $\mu =0.4$

Step 2: Determine the safe radius

For a safe turn without sliding,

$$\begin{gathered} \mu \ge \frac{v^2}{rg} \\ r\ge \frac{v^2}{\mu g} \end{gathered}$$

For the minimum value,

$$\begin{gathered} r=\frac{v^2}{\mu g} \\ =\frac{{12}^2}{0.4\times 10} \\ =\frac{144}{4} \\ =36m \end{gathered}$$

Therefore, option C is the correct option.