A girl holds a book of mass `m` against a vertical wall with a horizontal force `F` using her finger so that the book does not move. The frictional froce on the book by the wall is :

Options

A. `A` and along the finger but pointing towards the girl
B. `mu F` upwards where `mu` is the coefficeint of static friction
C. `mg` and upwards
D. equal and opposite to the resultant of `F` and `mg`

Explanation

To solve the problem, we need to analyze the forces acting on the book held against the wall.

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Book**:
- The weight of the book (W) acts downward and is given by \( W = mg \), where \( m \) is the mass of the book and \( g \) is the acceleration due to gravity.
- The girl applies a horizontal force \( F \) against the wall.
- There is a normal force \( N \) exerted by the wall on the book, which acts horizontally towards the left (opposite to the applied force).
- There is a frictional force \( f \) acting upwards, which prevents the book from sliding down the wall.

2. **Apply Newton's First Law**:
- Since the book is at rest, the net force acting on it must be zero. This means that the upward frictional force must balance the downward weight of the book.
- Therefore, we can write the equation:
\[ f = mg \]

3. **Determine the Frictional Force**:
- The frictional force \( f \) is the force exerted by the wall to prevent the book from sliding down. Since the book is not moving, the frictional force must equal the weight of the book.
- Thus, we conclude that:
\[ f = mg \]

4. **Conclusion**:
- The frictional force on the book by the wall is equal to the weight of the book, which is \( mg \).

### Final Answer:
The frictional force on the book by the wall is \( mg \).

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