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Which is true for rolling friction ( mu ...

Which is true for rolling friction `( mu _(r ) ) `, static friction `( mu_(s))` and kinetic friction `( mu_(k))` ?

A

(a)`mu_(s) gt mu_(k) gt mu_(r)`

B

(b)`mu_(s) lt mu_(k) lt mu_(r)`

C

(c)`mu_(s) lt mu_(k) gt mu_(r)`

D

(d)`mu_(s) gt mu_(k) gt mu_(r)`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question regarding the relationship between rolling friction (μ_r), static friction (μ_s), and kinetic friction (μ_k), let's analyze the properties of these types of friction step by step. ### Step-by-Step Solution: 1. **Understanding Friction Types**: - **Static Friction (μ_s)**: This is the friction that prevents an object from starting to move. It acts when a force is applied to an object at rest. - **Kinetic Friction (μ_k)**: This is the friction that acts on an object that is already in motion. It is usually less than static friction. - **Rolling Friction (μ_r)**: This is the friction that occurs when an object rolls over a surface. It is generally the least among the three types of friction. 2. **Comparing the Magnitudes**: - It is known from physics that: - The maximum static friction (μ_s) is greater than kinetic friction (μ_k) when an object is in motion. - Kinetic friction (μ_k) is greater than rolling friction (μ_r) when an object rolls. - Therefore, we can establish the following inequality: \[ μ_s > μ_k > μ_r \] 3. **Conclusion**: - Based on the above comparison, we can conclude that the relationship among the coefficients of friction is: \[ μ_s > μ_k > μ_r \] - This means that static friction is the greatest, followed by kinetic friction, and rolling friction is the least. ### Final Answer: The correct statement is: **μ_s > μ_k > μ_r**.
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