To determine which combination of statements about sliding friction is true, let's analyze each statement one by one. ### Statement Analysis **I. The frictional force is independent of the area of the surfaces in contact.** - **Explanation:** This statement is **true**. The frictional force does not depend on the contact area between two surfaces. Instead, it depends on the normal force (the perpendicular force pressing the two surfaces together) and the nature of the surfaces. This is because the microscopic interactions at the surface level are what primarily contribute to friction, and these interactions are not significantly affected by the area of contact. **II. The frictional force depends on the nature of the surfaces in contact.** - **Explanation:** This statement is also **true**. The type of materials in contact (e.g., rubber on concrete vs. ice on metal) affects the coefficient of friction, which is a measure of how much frictional force is generated for a given normal force. Different materials have different properties, such as roughness and hardness, which influence the frictional force. **III. The frictional force depends on the speed of sliding.** - **Explanation:** This statement is **generally false** for most practical cases of sliding friction. The static friction force is independent of speed, and for kinetic (sliding) friction, the frictional force remains relatively constant regardless of the speed of sliding, as long as the speed is not extremely high. At very high speeds, other factors like thermal effects and changes in surface characteristics may come into play, but these are not typical in standard physics problems. **IV. The frictional force is directly proportional to the normal reaction.** - **Explanation:** This statement is **true**. The frictional force (F_friction) can be expressed by the formula: \[ F_{\text{friction}} = \mu F_{\text{normal}} \] where \( \mu \) is the coefficient of friction (which depends on the materials in contact) and \( F_{\text{normal}} \) is the normal force. This shows that the frictional force is directly proportional to the normal force. ### Summary of Statements - **True Statements:** I, II, IV - **False Statement:** III ### Evaluating the Options Now, let's evaluate the options based on our analysis: - **A. I, III and IV**: This option is incorrect because III is false. - **B. I, II and IV**: This option is correct as all three statements are true. - **C. I, II and III**: This option is incorrect because III is false. - **D. II, III and IV**: This option is incorrect because III is false. ### Conclusion The correct answer is **B. I, II and IV**. ### Revision Summary - The frictional force is independent of the area of contact (True). - The frictional force depends on the nature of the surfaces in contact (True). - The frictional force does not depend on the speed of sliding under normal conditions (False). - The frictional force is directly proportional to the normal reaction force (True). Understanding these principles is crucial for solving problems related to friction in physics.