Maximum and minimum values of the resultant of two forces acting at a point are 7 N and 3 N respectively . The smaller force will be equal to

Options

A. 5 N
B. 4 N
C. 2 N
D. 1 N

Explanation

To solve the problem of finding the smaller force when the maximum and minimum resultant of two forces are given, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We have two forces, let's denote them as \( A \) and \( B \). The maximum resultant \( R_{max} \) is given as 7 N, and the minimum resultant \( R_{min} \) is given as 3 N.

2. **Use the Resultant Force Formulas**:
- The maximum resultant of two forces is given by:
\[ R_{max} = A + B \]
- The minimum resultant of two forces is given by:
\[ R_{min} = |A - B| \]

3. **Set Up the Equations**:
- From the maximum resultant:
\[ A + B = 7 \quad \text{(1)} \]
- From the minimum resultant:
\[ A - B = 3 \quad \text{(2)} \]

4. **Solve the Equations**:
- Add equations (1) and (2):
\[ (A + B) + (A - B) = 7 + 3 \]
\[ 2A = 10 \]
\[ A = 5 \, \text{N} \]

- Now substitute \( A \) back into equation (1) to find \( B \):
\[ 5 + B = 7 \]
\[ B = 7 - 5 \]
\[ B = 2 \, \text{N} \]

5. **Identify the Smaller Force**:
- The smaller force between \( A \) and \( B \) is:
\[ B = 2 \, \text{N} \]

### Final Answer:
The smaller force will be equal to **2 N**.

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