A block weighs W is held against a vertical wall by applying a horizontal force F. The minimum value of F needed to hold the block is

Options

A. less tha W
B. Equal to W
C. Greater than W
D. Data is insufficient

Explanation

To solve the problem of determining the minimum horizontal force \( F \) needed to hold a block weighing \( W \) against a vertical wall, we can analyze the forces acting on the block.

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Block**:
- The weight of the block \( W \) acts downward due to gravity.
- A horizontal force \( F \) is applied against the wall to hold the block in place.
- There is a frictional force \( f \) acting upward, which opposes the weight of the block.

2. **Understanding the Role of Friction**:
- The frictional force \( f \) can be expressed in terms of the normal force \( N \) exerted by the wall on the block. The relationship is given by:
\[ f = \mu N \]
where \( \mu \) is the coefficient of friction between the block and the wall.

3. **Determine the Normal Force**:
- In this scenario, the normal force \( N \) is equal to the applied horizontal force \( F \) since the wall is vertical and the force is applied horizontally. Thus, we have:
\[ N = F \]

4. **Equating Forces**:
- For the block to remain stationary and not slide down the wall, the upward frictional force must balance the downward weight of the block. Therefore, we can write:
\[ f = W \]
- Substituting the expression for friction, we get:
\[ \mu F = W \]

5. **Solving for the Minimum Force \( F \)**:
- Rearranging the equation gives us:
\[ F = \frac{W}{\mu} \]

6. **Analyzing the Coefficient of Friction**:
- The coefficient of friction \( \mu \) is a value that ranges between 0 and 1 (i.e., \( 0 < \mu < 1 \)). This means that:
\[ F = \frac{W}{\mu} > W \]
- Therefore, the minimum horizontal force \( F \) required to hold the block against the wall is greater than the weight of the block \( W \).

### Conclusion:
The minimum value of the horizontal force \( F \) needed to hold the block against the wall is greater than \( W \).

### Answer:
**Option 3: Greater than \( W \)**.