Question

A motor car has a width $1.1\text{m}$ between wheels. Its centre of gravity is $0.62\text{m}$ above the ground and the coefficient of friction between the wheels and the road is $0.8$. What is the maximum possible speed, if the centre of gravity inscribes a circle of radius $15\text{m}$ ? (Road surface is horizontal)

• A. $11.23\text{m/s}$
• B. $10.84\text{m/s}$
• C. $7.64\text{m/s}$
• D. $6.28\text{m/s}$

Answer 1

The correct option is B $10.84\text{m/s}$

Given:
Width of the car, $d=1.1m$,
Radius of the circular road,$R=15m$
Friction acting on the surface of the road,$\mu =0.8$
Let us consider the velocity of the car be $v$
Maximum centripetal force provided by friction will be $=\mu mg$
The frictional force is balanced by the centrifugal force acting outward.
Therefore,
$\mu mg=\frac{m{v}^2}{R}$

$v=\sqrt{\mu gR}$
Substituting all the values we get,

$v=\sqrt{0.8\times 9.8\times 15}$

$v=10.84\text{m/s}$

Hence, option $\left(C\right)$ is correct.