Question

the mechanical advantage of a wheel and axle is the radius of the wheel divided by the radius of the axle. on wheel and axle a, the wheel and axle are very close in size. on wheel and axle b, the radius of the wheel is much greater than the radius of the axle.
which wheel and axle has the greater mechanical advantage?

Explanation:

Step1: Define mechanical advantage

Let $MA$ = mechanical advantage, $r_w$ = wheel radius, $r_a$ = axle radius.
$MA = \frac{r_w}{r_a}$

Step2: Compare MA for A and B

For A: $r_w \approx r_a$, so $MA_A \approx \frac{r_a}{r_a} = 1$
For B: $r_w \gg r_a$, so $MA_B = \frac{r_w}{r_a} \gg 1$

Step3: Compare the two values

Since $MA_B \gg 1$ and $MA_A \approx 1$, $MA_B > MA_A$

Answer:

Wheel and axle B has the greater mechanical advantage.