The coefficient of friction between two surface is 0.2. The maximum angle of friction is

Options

A. (a)`sin^(-1)(0.2)`
B. (b)`cos^(-1)(0.2)`
C. (c)`tan^(-1)(0.1)`
D. (d)`cot^(-1)(5)`

Answer

To find the maximum angle of friction given the coefficient of friction, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The coefficient of friction (μ) is given as 0.2.

2. **Relate Coefficient of Friction to Angle of Friction**:
- The relationship between the coefficient of friction and the angle of friction (θ) is given by the formula:
\[ \mu = \tan(\theta) \]
- Here, θ is the angle of friction.

3. **Substitute the Given Value**:
- Substitute μ = 0.2 into the equation:
\[ 0.2 = \tan(\theta) \]

4. **Calculate the Angle θ**:
- To find θ, we take the arctangent (inverse tangent) of both sides:
\[ \theta = \tan^{-1}(0.2) \]

5. **Convert to Degrees (if necessary)**:
- Using a calculator, compute the value of θ:
\[ \theta \approx 11.31^\circ \]

6. **Conclusion**:
- The maximum angle of friction is approximately \( 11.31^\circ \).

### Final Answer:
The maximum angle of friction is \( \theta \approx 11.31^\circ \).

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