Question

A car is moving on a circular road of radius of curvature $500\text{m}$. If the coefficient of friction is $0.8$ and $g=10{\text{m/s}}^2$, the maximum speed of the car can have without slipping is in $\left(\text{km/hr}\right)$.

• A. $5\sqrt{10}$
• B. $20\sqrt{10}$
• C. $72\sqrt{10}$
• D. $54\sqrt{10}$

Answer 1

The correct option is C $72\sqrt{10}$

Given, radius of curvature $\left(r\right)=500\text{m}$
Coefficient of friction $\left(\mu \right)=0.8$

Condition for max speed of the car for not slipping is,

$\mu mg=\frac{m{v}_{max}^2}{r}$, here the frictional force will provide the necessary centripetal force
$\Rightarrow \left(v_{\text{max}}\right)=\sqrt{\mu rg}=\sqrt{0.8\times 500\times 10}=\sqrt{\frac{4}{5}\times 500\times 10}$
$=\sqrt{4\times 100\times 10}$
$=20\sqrt{10}\text{m/s}$ or $72\sqrt{10}\text{km/hr}$
$($As to convert $\left(\text{m/s}\right)$ to $\left(\text{km/hr}\right)$ we multiply it by $\frac{18}{5})$

Hence option C is the correct answer