Which affects racing car stability? Force F produces extension e in wire. If length & radius doubled, extension =?

Young's Modulus ($Y$) is given by:

where $F$ is the force, $A$ is the cross-sectional area, $e$ is the extension, and $L$ is the original length.
From this, the extension $e$ can be expressed as:

Since the cross-sectional area $A = \pi r^2$, we have:

Let the initial extension be $e_1$, initial length $L_1$, and initial radius $r_1$.

The new length is $L_2 = 2L_1$.
The new radius is $r_2 = 2r_1$.
The force $F$ and Young's Modulus $Y$ remain constant.

Substitute the new length and radius into the formula:

The new extension is half of the original extension.

The final answer is $\boxed{\text{C. e/2}}$.

On a frictionless inclined plane, the only force component causing acceleration down the plane is the component of gravity parallel to the plane.

The force parallel to the plane is $F_{parallel} = Mg \sin \theta$.
According to Newton's Second Law, $F_{parallel} = Ma$, where $a$ is the acceleration.

Cancel out the mass $M$ from both sides:

Given $g = 10 \text{ m/s}^2$ and $\theta = 30^\circ$.

We know that $\sin 30^\circ = 0.5$.

The acceleration of the block is $5 \text{ m/s}^2$.

The final answer is $\boxed{\text{C. 5 m/s}^2}$.