A horizontally force of 12 N pushes a 0.5kg book against a vertical wall. The book is initially at rest. If the coefficent of friction are `mu_(k)=0.6` and `mu_(s)=0.8` which of the following statements is true?

Options

A. The magnitude of the frictional force is 5N
B. The magnitude of the frictional force is 7.2N
C. The normal force is 5N
D. The book will start moving and accelerated

Answer

To solve the problem, we need to analyze the forces acting on the book when a horizontal force of 12 N is applied against a vertical wall. We will determine the frictional force and check which of the given statements is true.

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Book:**
- The weight of the book (mg) acting downward.
- The applied horizontal force (F) of 12 N pushing the book against the wall.
- The normal force (N) exerted by the wall on the book, acting horizontally away from the wall.
- The frictional force (f) acting upward to prevent the book from sliding down.

2. **Calculate the Weight of the Book:**
\[ m = 0.5 \, \text{kg} \]
\[ g = 10 \, \text{m/s}^2 \]
\[ \text{Weight (mg)} = m \cdot g = 0.5 \cdot 10 = 5 \, \text{N} \]

3. **Determine the Normal Force:**
- The normal force (N) is equal to the applied horizontal force (F) since the book is in equilibrium in the horizontal direction.
\[ N = F = 12 \, \text{N} \]

4. **Calculate the Maximum Static Friction:**
\[ \mu_s = 0.8 \quad (\text{coefficient of static friction}) \]
\[ f_{\text{max}} = \mu_s \cdot N = 0.8 \cdot 12 = 9.6 \, \text{N} \]

5. **Compare the Weight of the Book with Maximum Static Friction:**
- The weight of the book (5 N) is less than the maximum static friction (9.6 N). Therefore, the book will not slide down.

6. **Determine the Actual Frictional Force:**
- Since the book is at rest and only 5 N of force is required to balance the weight, the actual frictional force (f) will be equal to the weight of the book.
\[ f = 5 \, \text{N} \]

7. **Conclusion:**
- The frictional force acting on the book is 5 N, which is sufficient to keep the book at rest against the wall.

### Final Answer:
The correct statement is: **The magnitude of frictional force is 5 N.**