A block weighing 10 kg just starts sliding down a rough inclined plane, which rises 5 in every 13 . What is the coefficient of friction ?

Options

A. 0.325
B. 0.515
C. 0.416
D. 0.632

Explanation

To find the coefficient of friction (μ) for a block weighing 10 kg that just starts sliding down a rough inclined plane, we can follow these steps:

### Step 1: Understand the Geometry of the Inclined Plane
The inclined plane rises 5 meters for every 13 meters of horizontal distance. This gives us the rise/run ratio, which helps us determine the angle of the incline (θ).

### Step 2: Calculate the Angle of Incline (θ)
Using the rise/run ratio:
- Rise = 5 m
- Run = 13 m

We can find the angle θ using the tangent function:
\[ \tan(\theta) = \frac{\text{rise}}{\text{run}} = \frac{5}{13} \]

### Step 3: Calculate θ
To find θ, we take the arctangent:
\[ \theta = \tan^{-1}\left(\frac{5}{13}\right) \]
Calculating this gives:
\[ \theta \approx 22.61^\circ \]

### Step 4: Relate θ to the Coefficient of Friction (μ)
The angle of repose (θ) is related to the coefficient of friction (μ) by the formula:
\[ \tan(\theta) = \mu \]

### Step 5: Calculate the Coefficient of Friction (μ)
Using the value of θ we found:
\[ \mu = \tan(22.61^\circ) \approx \frac{5}{13} \approx 0.3846 \]

### Step 6: Round the Coefficient of Friction
For practical purposes, we can round the coefficient of friction to three decimal places:
\[ \mu \approx 0.385 \]

### Final Answer
The coefficient of friction (μ) is approximately 0.385.

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