In a setup where a 13 mm diameter bar is inserted into a 25 mm diameter coil, the fill factor is:

To determine the fill factor in this scenario, you need to understand how it is calculated. The fill factor is defined as the ratio of the area occupied by the object (in this case, the bar) to the area of the space it occupies (the coil).

The area of the bar can be calculated using the formula for the area of a circle, A = πr². For the bar with a diameter of 13 mm, the radius is 6.5 mm, which gives an area of approximately 132.73 mm².

The area of the coil, also calculated using the area formula, has a diameter of 25 mm, resulting in a radius of 12.5 mm and an area of approximately 490.87 mm².

The fill factor is then calculated by dividing the area of the bar by the area of the coil:

Fill Factor = Area of the bar / Area of the coil

Fill Factor = 132.73 mm² / 490.87 mm² ≈ 0.27 (or 27%).

While this specific value of 0.27 isn't in the choices, the closest option that represents a significant relationship between the areas, in relation to the provided options, is