A block of mass 'M' is pressed against a wall with a horizontal force F. Then
a) it will slide down if the wall is smooth
b) frictional force may balance the weight if the wall is rough
c) Normal reaction is equal to weight of the block
d) Normal reaction is zero if the wall is smooth

Options

A. a and b are correct
B. c and d are correct
C. a and d are correct
D. b and c are correct

Answer

To solve the problem, we will analyze the situation step by step and evaluate each statement provided in the question.

### Given:
- A block of mass 'M' is pressed against a wall with a horizontal force 'F'.
- We need to assess four statements regarding the block's behavior against the wall.

### Step 1: Analyze the forces acting on the block
1. **Identify the forces**:
- The block experiences a horizontal force \( F \) pushing it against the wall.
- There is a normal force \( N \) exerted by the wall on the block, acting perpendicular to the wall.
- The weight of the block \( W = mg \) acts downwards due to gravity.
- If the wall is smooth, there is no frictional force acting on the block.

### Step 2: Free Body Diagram (FBD)
2. **Draw the FBD**:
- Draw the block on the wall.
- Show the force \( F \) acting horizontally towards the wall.
- Show the normal force \( N \) acting horizontally away from the wall.
- Show the weight \( W = mg \) acting downwards.

### Step 3: Evaluate each statement
3. **Statement (a)**: "It will slide down if the wall is smooth."
- Since there is no friction to counteract the weight of the block, the block will slide down the wall due to gravity.
- **Conclusion**: This statement is **true**.

4. **Statement (b)**: "Frictional force may balance the weight if the wall is rough."
- If the wall is rough, a frictional force \( f \) can act upwards. The maximum static friction is given by \( f_{max} = \mu N \), where \( \mu \) is the coefficient of friction.
- If \( f \) is sufficient to balance the weight \( mg \), the block will not slide down. However, if \( f < mg \), the block will slide down.
- **Conclusion**: This statement is **true** (it may balance the weight).

5. **Statement (c)**: "Normal reaction is equal to weight of the block."
- The normal force \( N \) is equal to the horizontal force \( F \) applied against the wall, not the weight of the block.
- **Conclusion**: This statement is **false**.

6. **Statement (d)**: "Normal reaction is zero if the wall is smooth."
- The normal force \( N \) is not zero; it is equal to the applied force \( F \). The smoothness of the wall does not affect the normal force.
- **Conclusion**: This statement is **false**.

### Final Conclusion:
- The correct statements are (a) and (b).
- The incorrect statements are (c) and (d).

### Summary of Answers:
- a) True
- b) True
- c) False
- d) False