A block of mass `10kg` is placed on a rough horizontal surface having coefficient of friction `mu=0.5` . If a horizontal force of `100N` is acting on it, then acceleration of the block will be.

Options

A. `10"ms"^(-2)`
B. `5"ms"^(-2)`
C. `15"ms"^(-2)`
D. `0.5"ms"^(-2)`

Explanation

To solve the problem step by step, we can follow these calculations:

### Step 1: Identify the given values
- Mass of the block (m) = 10 kg
- Coefficient of friction (μ) = 0.5
- Applied horizontal force (F) = 100 N
- Acceleration due to gravity (g) = 10 m/s² (assuming standard value)

### Step 2: Calculate the normal force (N)
The normal force acting on the block is equal to the weight of the block, which can be calculated using the formula:
\[ N = m \cdot g \]
Substituting the values:
\[ N = 10 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 100 \, \text{N} \]

### Step 3: Calculate the maximum frictional force (f)
The maximum frictional force can be calculated using the formula:
\[ f_{\text{max}} = \mu \cdot N \]
Substituting the values:
\[ f_{\text{max}} = 0.5 \cdot 100 \, \text{N} = 50 \, \text{N} \]

### Step 4: Determine the net force acting on the block
The net force (F_net) acting on the block can be found by subtracting the frictional force from the applied force:
\[ F_{\text{net}} = F - f_{\text{max}} \]
Substituting the values:
\[ F_{\text{net}} = 100 \, \text{N} - 50 \, \text{N} = 50 \, \text{N} \]

### Step 5: Calculate the acceleration (a) of the block
Using Newton's second law, the acceleration can be calculated as:
\[ F_{\text{net}} = m \cdot a \]
Rearranging the formula gives:
\[ a = \frac{F_{\text{net}}}{m} \]
Substituting the values:
\[ a = \frac{50 \, \text{N}}{10 \, \text{kg}} = 5 \, \text{m/s}^2 \]

### Final Answer
The acceleration of the block is \( 5 \, \text{m/s}^2 \).

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