If `mu_(s), mu_(k)` and `mu_(r)` are the coefficients of static, kinetic and rolling friction respectively then

Options

A. `mu_(s) gt mu_(k) lt mu_(r)`
B. `mu_(s) lt mu_(k) gt mu_(r)`
C. `mu_(s) gt mu_(k) gt mu_(r)`
D. `mu_(s) = mu_(k) = mu_(r)`

Answer

To solve the problem regarding the relationship between the coefficients of static friction (μ_s), kinetic friction (μ_k), and rolling friction (μ_r), we can follow these steps:

### Step 1: Understand the definitions
- **Static Friction (μ_s)**: This is the frictional force that must be overcome to start moving an object at rest. It is generally higher than the other types of friction because it needs to overcome the inertia of the object.
- **Kinetic Friction (μ_k)**: This is the frictional force acting on an object that is already in motion. It is usually less than static friction because once an object is in motion, it requires less force to keep it moving.
- **Rolling Friction (μ_r)**: This is the frictional force that occurs when an object rolls over a surface. It is the least among the three types of friction because rolling motion requires the least amount of frictional force to maintain motion.

### Step 2: Establish the relationships
From the definitions above, we can establish the following relationships based on the nature of friction:
- Since static friction must overcome inertia, it is the highest:
\[ \mu_s > \mu_k \]
- Kinetic friction is less than static friction because it acts on moving objects:
\[ \mu_k > \mu_r \]
- Rolling friction is the least because it involves rolling rather than sliding:
\[ \mu_r < \mu_k \]

### Step 3: Combine the relationships
Combining all the relationships, we can conclude:
\[ \mu_s > \mu_k > \mu_r \]

### Final Conclusion
Thus, the correct relation among the coefficients of friction is:
\[ \mu_s > \mu_k > \mu_r \]