Correct Option
The correct option isA sharp knife has a smaller contact area, exerting higher pressure.
Explanation
The principle behind the cutting action of a knife is based on the physical quantity Pressure. Pressure is defined as the force applied perpendicular to the surface of an object per unit area. Mathematically, it is expressed as:
Pressure (P) = Force (F) / Area (A)
This relationship indicates that pressure is directly proportional to the applied force and inversely proportional to the contact area.
Option Analysis
- A sharp knife exerts more force. is incorrect: The force exerted depends on the external effort applied by the user, not on the sharpness of the knife itself. A sharp knife requires less force to achieve the same result, but it does not inherently exert more force.
- A sharp knife has less mass. is incorrect: The mass of the knife is not the primary factor determining its cutting ability. A heavy but blunt object will not cut as effectively as a lighter but sharper object because the force is distributed over a larger area.
- A sharp knife has a smaller contact area, exerting higher pressure. is correct: A sharp knife has an extremely thin cutting edge, which results in a very small surface area of contact. According to the formula \( P = F/A \), for a given amount of force, a smaller area results in significantly higher pressure. This high pressure allows the knife to pierce through the material easily.
- A sharp knife reduces friction. is incorrect: While friction affects how easily a blade slides through material, the fundamental reason a sharp knife cuts better is the concentration of force (pressure), not the reduction of friction.
Key Takeaway
Pressure is inversely proportional to the area of contact. Reducing the surface area (sharpening the edge) increases the pressure exerted for the same amount of applied force, facilitating cutting.