A body of mass 10 kg moves on rough horizontal surface with initial velocity 10m/s and travels 500m before coming to rest. The coefficient of friction is

Options

A. `0.1`
B. `0.5`
C. `0.05`
D. `0.01`

Answer

To solve the problem, we need to find the coefficient of friction (μ) for a body of mass 10 kg that comes to rest after traveling 500 m on a rough horizontal surface with an initial velocity of 10 m/s.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of the body (m) = 10 kg
- Initial velocity (u) = 10 m/s
- Final velocity (v) = 0 m/s (since it comes to rest)
- Distance traveled (s) = 500 m

2. **Use the Kinematic Equation:**
We can use the kinematic equation to find the acceleration (a) of the body:
\[ v^2 = u^2 + 2as \]
Substituting the known values:
\[ 0 = (10)^2 + 2a(500) \]
This simplifies to:
\[ 0 = 100 + 1000a \]
Rearranging gives:
\[ 1000a = -100 \quad \Rightarrow \quad a = -\frac{100}{1000} = -0.1 \, \text{m/s}^2 \]

3. **Relate Acceleration to Friction:**
The acceleration due to friction can be expressed as:
\[ a = -\mu g \]
where \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)). Therefore:
\[ -0.1 = -\mu \cdot 9.81 \]
This leads to:
\[ \mu = \frac{0.1}{9.81} \]

4. **Calculate the Coefficient of Friction:**
Now, we can calculate μ:
\[ \mu \approx \frac{0.1}{9.81} \approx 0.0102 \]

5. **Final Answer:**
The coefficient of friction (μ) is approximately \( 0.0102 \).