A door 1.6 m wide requires a force of 1 N to be applied at the free end to open or close it. The force that is required at a point 0.4 m distant from the hinges for opening or closing the door is

Options

A. 1.2 N
B. 3.6 N
C. 2.5 N
D. 4 N

Explanation

To solve the problem, we need to determine the force required to open or close a door when the force is applied at a distance of 0.4 m from the hinges, given that a force of 1 N is required at the free end (1.6 m from the hinges).

### Step-by-Step Solution:

1. **Understand the Torque Concept**:
Torque (T) is defined as the product of the force (F) applied and the distance (r) from the pivot point (hinges). The formula for torque is:
\[ T = F \times r \]

2. **Calculate the Torque at the Free End**:
Given that a force of 1 N is applied at the free end of the door (1.6 m from the hinges):
\[ T = 1 \, \text{N} \times 1.6 \, \text{m} = 1.6 \, \text{Nm} \]

3. **Set Up the Equation for the Force at 0.4 m**:
Now, we need to find the force \( F \) that must be applied at a distance of 0.4 m from the hinges to produce the same torque of 1.6 Nm:
\[ T = F \times 0.4 \, \text{m} \]

4. **Equate the Two Torque Values**:
Since both torques must be equal for the door to open or close in the same manner:
\[ F \times 0.4 = 1.6 \]

5. **Solve for F**:
Rearranging the equation to solve for \( F \):
\[ F = \frac{1.6}{0.4} = 4 \, \text{N} \]

6. **Conclusion**:
The force required at a point 0.4 m distant from the hinges to open or close the door is 4 N.

### Final Answer:
The required force is **4 N**.

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