Question

A car is moving on a circular level road of radius of curvature $300\text{m}$. If the coefficient of friction is $0.5$ and taking $g=10{\text{m/s}}^2$, the maximum speed the car can have (in $\text{km/hr}$) is

• A. $278.9\text{km/h}$
• B. $0.45\text{km/h}$
• C. $139.4\text{km/h}$
• D. $1\text{km/h}$

Answer 1

The correct option is C $139.4\text{km/h}$

FBD of car:

Given,
Radius of curvature $\left(r\right)=300\text{m}$
Coefficient of friction $\left(\mu \right)=0.5$

$N=mg$ i.e forces are balanced in vertical direction.
Along the radial direction, we have
$f=\frac{m{v}^2}{r}$ i.e friction provides the centripetal force.
$f=\mu N=\mu mg$ (limiting condition, when the car has maximum velocity and is just about to slip)
i.e $\mu mg=\frac{m{v}_{max}^2}{r}$
$\Rightarrow v_{\text{max}}=\sqrt{\mu rg}$
$=\sqrt{0.5\times 300\times 10}=38.72\text{m/s}$
$=139.4\text{km/h}$