A modern grand-prix racing car of mass m is travelling on a flat...

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 ${F}_{L}$ acting downwards on the car is:

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 .

Options

A $m\left(\dfrac{{v}^{2}}{{\mu}_{s}R} + g\right)$
B $m\left(\dfrac{{v}^{2}}{{\mu}_{s}R} - g\right)$
C $m\left(g - \dfrac{{v}^{2}}{{\mu}_{s}R}\right)$
D $- m\left(g + \dfrac{{v}^{2}}{{\mu}_{s}R}\right)$

Correct answer

B. $m\left(\dfrac{{v}^{2}}{{\mu}_{s}R} - g\right)$

Step-by-step solution

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

$N = \dfrac{m{v}^{2}}{{\mu}_{s}R} = mg + {F}_{L}$

${F}_{L} = \dfrac{m{v}^{2}}{{\mu}_{s}R} - mg$

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