A block of weight 5 N is pushed against a vertical wall by a force 12 N . The coefficient of friction between the wall and block is `0.6` . Find the magnitude of the force exerted by the wall on the block :

Options

A. 12 N
B. 5 N
C. 7.2 N
D. 13 N

Explanation

To solve the problem, we need to find the total force exerted by the wall on the block. Let's break it down step by step.

### Step 1: Identify the Forces Acting on the Block
- The weight of the block (W) acting downwards = 5 N.
- The applied force (F) pushing the block against the wall = 12 N.
- The normal force (N) exerted by the wall on the block, which acts horizontally and is equal in magnitude to the applied force = 12 N.
- The frictional force (f) acting upwards, which opposes the weight of the block.

### Step 2: Calculate the Maximum Frictional Force
The maximum frictional force can be calculated using the formula:
\[ f_{\text{max}} = \mu \cdot N \]
Where:
- \(\mu\) = coefficient of friction = 0.6
- \(N\) = normal force = 12 N

Substituting the values:
\[ f_{\text{max}} = 0.6 \cdot 12 = 7.2 \, \text{N} \]

### Step 3: Compare the Weight and Frictional Force
The weight of the block is 5 N, and the maximum frictional force is 7.2 N. Since the maximum frictional force is greater than the weight of the block, the frictional force will be equal to the weight of the block in this case to maintain equilibrium.

Thus, the frictional force (f) acting upwards is:
\[ f = W = 5 \, \text{N} \]

### Step 4: Calculate the Total Force Exerted by the Wall
The total force exerted by the wall on the block consists of two components:
1. The normal force (N) = 12 N (horizontal)
2. The frictional force (f) = 5 N (vertical)

To find the resultant force (F_net) exerted by the wall on the block, we can use the Pythagorean theorem:
\[ F_{\text{net}} = \sqrt{N^2 + f^2} \]

Substituting the values:
\[ F_{\text{net}} = \sqrt{(12)^2 + (5)^2} \]
\[ F_{\text{net}} = \sqrt{144 + 25} \]
\[ F_{\text{net}} = \sqrt{169} \]
\[ F_{\text{net}} = 13 \, \text{N} \]

### Final Answer
The magnitude of the force exerted by the wall on the block is **13 N**.

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