Consider a car that overturns while taking a turn. Select the option that is experienced by the wheels of the car

The correct answer is: First, the inner wheel leaves the ground.

To understand why the inner wheels leave the ground first when a car overturns while taking a turn, we need to analyze the forces and torques acting on the car during the turn.

Let us consider a car of mass $M$ making a turn of radius $R$ at a constant speed $v$. The center of gravity of the car is at a height $h$ above the ground, and the distance between the inner and outer wheels (the track width) is $2a$.

When the car takes a turn, two main forces create moments (torques) about the center of gravity or the contact points of the wheels:
1. Centrifugal Force: In the rotating frame of the car, an outward centrifugal force acts at the center of gravity, given by:
$F_c=\frac{M{v}^2}{R}$
This force acts horizontally outwards and creates a clockwise overturning torque of magnitude $F_c\times h$ about the wheel contact points.
2. Gravity: The weight of the car $W=Mg$ acts vertically downwards through the center of gravity, which provides a restoring torque (counter-clockwise) keeping the car stable.

Due to the overturning torque, vertical reaction forces from the ground on the inner wheels ($R_i$) and outer wheels ($R_o$) change. By taking moments about the outer wheel contact point, we find the reaction force on the inner wheels:
$R_i=\frac{Mg}{2}-\frac{M{v}^{2}h}{2Ra}$
Similarly, the reaction force on the outer wheels is:
$R_o=\frac{Mg}{2}+\frac{M{v}^{2}h}{2Ra}$

As the speed of the car $v$ increases, the term representing the transfer of load due to the centrifugal force increases. Consequently, the normal reaction on the inner wheels $R_i$ decreases, while the normal reaction on the outer wheels $R_o$ increases.

At a critical speed, the normal reaction on the inner wheels becomes zero ($R_i=0$). At this exact moment, the inner wheels lose contact with the ground and lift off. Since $R_o$ increases during this process, the outer wheels remain firmly pressed against the ground, meaning the inner wheel must leave the ground first.