A force of 20 N acts on a body and the body moves through 1 m at an angle of` 45^(@)` in the direction of the force. The work done by the force is

Options

A. `10 sqrt(2)` J
B. `(10)/(sqrt(2)) ` J
C. `- 10 sqrt(2) ` J
D. `(-10)/(sqrt(2)) ` J

Explanation

To solve the problem of calculating the work done by a force acting on a body, we can follow these steps:

### Step 1: Understand the Given Information
We have:
- Force (F) = 20 N
- Displacement (s) = 1 m
- Angle (θ) = 45° (the angle between the force and the direction of displacement)

### Step 2: Use the Work Done Formula
The work done (W) by a force is given by the formula:
\[ W = F \cdot s \cdot \cos(\theta) \]
where:
- \( F \) is the force applied,
- \( s \) is the displacement,
- \( \theta \) is the angle between the force and the direction of displacement.

### Step 3: Substitute the Values into the Formula
Now, substituting the known values into the formula:
\[ W = 20 \, \text{N} \cdot 1 \, \text{m} \cdot \cos(45°) \]

### Step 4: Calculate \( \cos(45°) \)
The value of \( \cos(45°) \) is:
\[ \cos(45°) = \frac{1}{\sqrt{2}} \approx 0.707 \]

### Step 5: Substitute \( \cos(45°) \) into the Equation
Now, substituting this value back into the work done equation:
\[ W = 20 \cdot 1 \cdot \frac{1}{\sqrt{2}} \]
\[ W = \frac{20}{\sqrt{2}} \, \text{J} \]

### Step 6: Rationalize the Denominator
To simplify \( \frac{20}{\sqrt{2}} \), we multiply the numerator and denominator by \( \sqrt{2} \):
\[ W = \frac{20 \sqrt{2}}{2} \, \text{J} \]
\[ W = 10 \sqrt{2} \, \text{J} \]

### Final Answer
Thus, the work done by the force is:
\[ W = 10\sqrt{2} \, \text{J} \]

---