The limiting frictional force between two surfaces depends on I. the cohesive force of the material II. the…

Analysis of the Question

The question asks us to identify the factors that influence the limiting frictional force (the maximum static friction) between two surfaces. We need to evaluate the three statements provided:

• I. The cohesive force of the material: This relates to the molecular attraction between the surfaces.
• II. The nature of the surfaces in contact: This refers to the roughness or smoothness of the surfaces (often represented by the coefficient of friction, $\mu$).
• III. The relative velocity between the surfaces: This refers to how fast one surface is moving over the other.

Concept Explanation

Friction is a force that opposes motion. The limiting frictional force ($F_L$) is defined by the formula:

Where:

• $\mu$ (Coefficient of friction): This is determined by the nature of the surfaces in contact (e.g., wood on wood vs. steel on ice).
• $R$ (Normal reaction): This is the force pressing the two surfaces together.

Evaluating the statements:

1. Cohesive force (I): While molecular forces contribute to the nature of the surface, "limiting friction" in standard physics curricula is primarily defined by the nature of the surfaces and the normal reaction, not the cohesive force of the bulk material itself.
2. Nature of the surfaces (II): This is the primary factor. Different materials have different coefficients of friction ($\mu$). This is definitely a factor.
3. Relative velocity (III): Limiting friction is the force required to start motion. Once motion begins, we talk about kinetic friction. The limiting frictional force is independent of the speed or relative velocity between the surfaces.

Step-by-Step Solution

• Step 1: Identify the formula for limiting friction: $F_L = \mu R$.
• Step 2: Analyze the variables. $\mu$ depends on the nature of the surfaces (Statement II). $R$ depends on the weight or applied pressure.
• Step 3: Compare with the options. Statement II is correct. Statement III is incorrect because limiting friction is independent of velocity (it is a static condition). Statement I is generally considered a property of the material's surface, but in the context of standard JAMB physics, the "nature of the surfaces" is the standard accepted factor.
• Step 4: Looking at the options provided, Option B (II only) is the most accurate representation of the factors affecting limiting friction.

Conclusion

The limiting frictional force is independent of the area of contact and the relative velocity. It depends on the nature of the surfaces (the coefficient of friction) and the normal reaction. Therefore, only statement II is correct.

Exam Tip: Always remember that friction is independent of the surface area and independent of the velocity of the sliding object. If you see these in a question, you can immediately rule them out!