Question

A modern Grand Prix racing car of mass $m$ is travelling on a flat track in a circular arc of radius $R$ with a speed $v$. If the coefficient of static friction between the tyres and the track is ${\mu }_s$, then the magnitude of negative lift $F_1$ acting downwards on the car is -

$($Assume forces on the four tyres are identical and $g=$ acceleration due to gravity$)$

• A. $m(\frac{v^2}{{\mu }_{s}R}-g)$
• B. $m(\frac{v^2}{{\mu }_{s}R}+g)$
• C. $m(g-\frac{v^2}{{\mu }_{s}R})$
• D. $-m(g+\frac{v^2}{{\mu }_{s}R})$

Answer 1

The correct option is A $m(\frac{v^2}{{\mu }_{s}R}-g)$

On drawing the FBD of the car,


Applying the condition of equilibrium along the radial direction,

$f=\frac{m{v}^2}{R}$

$\Rightarrow {\mu }_{s}N=\frac{m{v}^2}{R}$

$\Rightarrow {\mu }_s(mg+F_L)=\frac{m{v}^2}{R}$

$\Rightarrow F_L=m(\frac{v^2}{{\mu }_{s}R}-g)$

Hence, option $\left(A\right)$ is the correct answer.