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

Explanation

To find the value of \( x \) (the smaller force) when the maximum and minimum resultant forces of two forces acting at a point are given as 7 N and 3 N, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Forces**:
Let \( P \) be the larger force and \( Q \) be the smaller force. According to the problem, we have:
\[ P + Q = 7 \, \text{N} \quad \text{(maximum resultant)} \]
\[ P - Q = 3 \, \text{N} \quad \text{(minimum resultant)} \]

2. **Set Up the Equations**:
From the maximum and minimum resultant equations, we can write:
\[ P + Q = 7 \quad \text{(1)} \]
\[ P - Q = 3 \quad \text{(2)} \]

3. **Add the Two Equations**:
By adding equations (1) and (2), we can eliminate \( Q \):
\[ (P + Q) + (P - Q) = 7 + 3 \]
This simplifies to:
\[ 2P = 10 \]
Thus, we find:
\[ P = 5 \, \text{N} \]

4. **Substitute \( P \) Back to Find \( Q \)**:
Now, substitute \( P \) back into equation (1):
\[ 5 + Q = 7 \]
Solving for \( Q \):
\[ Q = 7 - 5 = 2 \, \text{N} \]

5. **Identify the Smaller Force**:
Since \( Q \) is the smaller force, we have:
\[ x = Q = 2 \, \text{N} \]

### Final Answer:
The value of \( x \) is \( 2 \, \text{N} \).

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