The coefficient of static friction has no units

Both (A) and (R) are true and (R) is the correct explanation of (A)

The coefficient of static friction is a dimensionless scalar that quantifies the ratio of the maximum static frictional force (F) between two surfaces to the normal force (N) pressing them together. This relationship is expressed as:

μ_s = F / N

Since both the frictional force and the normal force are measured in units of force (such as newtons), their ratio is unitless, making the coefficient of static friction a dimensionless quantity. This coefficient indicates how much force is required to initiate motion between two stationary objects in contact. A higher coefficient suggests that greater force is needed to overcome static friction, while a lower coefficient indicates that less force is required.

It's important to note that the coefficient of static friction is specific to the pair of materials in contact and can vary based on factors such as surface roughness and the presence of lubricants. For example, the coefficient of static friction between rubber and concrete is typically higher than that between ice and steel, reflecting the differences in the ease with which these material pairs can be set into relative motion.