A body of mass 2kg is placed on a horizontal surface having kinetic friction `0.4` and static friction `0.5` . If the force applied on the body is `2.5N` , then the frictional force acting on the body will be

Options

A. 8N
B. 10N
C. 20N
D. 2.5N

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Identify the Given Information
- Mass of the body (m) = 2 kg
- Coefficient of static friction (µs) = 0.5
- Coefficient of kinetic friction (µk) = 0.4
- Applied force (F) = 2.5 N

### Step 2: Calculate the Normal Force (N)
The normal force (N) acting on the body can be calculated using the formula:
\[ N = m \cdot g \]
where \( g \) (acceleration due to gravity) is approximately \( 10 \, \text{m/s}^2 \).

Substituting the values:
\[ N = 2 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 20 \, \text{N} \]

### Step 3: Calculate the Maximum Static Friction Force (Fs max)
The maximum static friction force can be calculated using the formula:
\[ F_{s \, \text{max}} = \mu_s \cdot N \]

Substituting the values:
\[ F_{s \, \text{max}} = 0.5 \cdot 20 \, \text{N} = 10 \, \text{N} \]

### Step 4: Compare the Applied Force with Maximum Static Friction
The applied force (F) is 2.5 N, which is less than the maximum static friction force (Fs max) of 10 N.

### Step 5: Determine the Frictional Force
Since the applied force (2.5 N) is less than the maximum static friction (10 N), the frictional force will equal the applied force. Therefore, the frictional force acting on the body is:
\[ F_{\text{friction}} = F = 2.5 \, \text{N} \]

### Final Answer
The frictional force acting on the body is **2.5 N**.

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