A 100 N force acts horizontally on a block of 10 kg placed on a horizontal rough surface of coefficient of friction `mu=0.5`. If the acceleration due to gravity (g) is taken as `10ms^(-2)`, the acceleration of the block (in `ms^(-2)`) is

Options

A. 2.5
B. 10
C. 5
D. 7.5

Explanation

To solve the problem step by step, we will follow the principles of Newton's laws of motion, particularly focusing on the forces acting on the block and calculating the resulting acceleration.

### Step 1: Identify the Forces Acting on the Block
The forces acting on the block are:
- The applied force (F) = 100 N (acting horizontally)
- The frictional force (f) opposing the motion
- The weight of the block (W) = mass (m) × gravity (g)

Given:
- Mass of the block, \( m = 10 \, \text{kg} \)
- Coefficient of friction, \( \mu = 0.5 \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)

### Step 2: Calculate the Weight of the Block
The weight of the block can be calculated using the formula:
\[ W = m \times g \]
Substituting the values:
\[ W = 10 \, \text{kg} \times 10 \, \text{m/s}^2 = 100 \, \text{N} \]

### Step 3: Calculate the Normal Force
On a horizontal surface, the normal force (N) is equal to the weight of the block:
\[ N = W = 100 \, \text{N} \]

### Step 4: Calculate the Frictional Force
The frictional force (f) can be calculated using the formula:
\[ f = \mu \times N \]
Substituting the values:
\[ f = 0.5 \times 100 \, \text{N} = 50 \, \text{N} \]

### Step 5: Determine the Net Force Acting on the Block
The net force (F_net) acting on the block can be calculated by subtracting the frictional force from the applied force:
\[ F_{\text{net}} = F - f \]
Substituting the values:
\[ F_{\text{net}} = 100 \, \text{N} - 50 \, \text{N} = 50 \, \text{N} \]

### Step 6: Calculate the Acceleration of the Block
Using Newton's second law, the acceleration (a) can be calculated using the formula:
\[ F_{\text{net}} = m \times a \]
Rearranging the formula to solve for acceleration:
\[ a = \frac{F_{\text{net}}}{m} \]
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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