If a ladder weighting `250 N` in placed a smooth vertical wall having coefficient of friction between it and floor 0.3, then what is the maximum force of friction available at the point of contact between the ladder and the floor? a) 75 N b) 50 N c) 35 N d) 25 N

Options

A. `75 N`
B. `50 N`
C. `35 N`
D. `25 N`

Explanation

To solve the problem, we need to determine the maximum force of friction available at the point of contact between the ladder and the floor. Here are the steps to arrive at the solution:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Weight of the ladder (W) = 250 N
- Coefficient of friction (μ) = 0.3

2. **Understand the Forces Acting on the Ladder:**
- The ladder has a weight acting downwards, which is balanced by the normal reaction force (R) from the floor acting upwards.
- Since the wall is smooth, it does not exert any horizontal friction force on the ladder.

3. **Establish the Relationship Between Normal Force and Friction:**
- The maximum force of friction (F) can be calculated using the formula:
\[ F = \mu \cdot R \]
- Here, R is the normal reaction force, which is equal to the weight of the ladder (W) since there are no vertical accelerations.

4. **Calculate the Normal Reaction Force (R):**
- Since the ladder is in equilibrium:
\[ R = W = 250 \, \text{N} \]

5. **Substitute Values into the Friction Formula:**
- Now, substitute the values into the friction formula:
\[ F = \mu \cdot R = 0.3 \cdot 250 \, \text{N} \]

6. **Perform the Calculation:**
- Calculate the maximum force of friction:
\[ F = 0.3 \cdot 250 = 75 \, \text{N} \]

7. **Conclusion:**
- The maximum force of friction available at the point of contact between the ladder and the floor is **75 N**.

### Final Answer:
- The correct option is **a) 75 N**.