What is the relationship between the radius of a wheel and the axle in terms of mechanical advantage?

The relationship between the radius of a wheel and the axle directly impacts mechanical advantage, which is a key principle in simple machines. When the radius of the wheel is larger compared to the axle, the mechanical advantage increases. This benefit arises because a larger wheel allows for greater force to be applied over a longer distance, thus requiring less input force to lift a certain load.

In practical terms, when using a wheel and axle system, the mechanical advantage is calculated based on the radii of the wheel and axle. For instance, if the radius of the wheel is double that of the axle, the mechanical advantage is effectively two, meaning you can lift twice the weight with the same amount of input effort. This principle is critical in applications such as vehicles and machinery, where maximizing efficiency and force is desirable.

The other options either misinterpret this relationship or introduce concepts that do not directly apply to mechanical advantage in this context.