1. Identify the forces on the car

On a flat track, the car moves in a circle of radius $R$ with speed $v$.

The forces acting vertically are:

• Weight downward: $mg$
• Negative lift downward: $F_L$
• Normal reaction upward: $N$

Since there is no vertical acceleration, $N = mg + F_L$

2. Centripetal force requirement

The required centripetal force is provided by static friction: $f = \frac{mv^2}{R}$

Maximum available static friction is $f_{\max} = \mu_s N$

For the car to just negotiate the curve at speed $v$, $\mu_s N = \frac{mv^2}{R}$

Substitute $N = mg + F_L$: $\mu_s (mg + F_L) = \frac{mv^2}{R}$

3. Solve for $F_L$

$mg + F_L = \frac{mv^2}{\mu_s R}$

$F_L = \frac{mv^2}{\mu_s R} - mg$

$F_L = m\left(\frac{v^2}{\mu_s R} - g\right)$

4. Match with the options

This matches: $\boxed{m\left(\frac{v^2}{\mu_s R} - g\right)}$

So the correct option is C.