A body moves a distance of 10 m along a straight line under an action of 5 N force. If work done is 25 J, then angle between the force and firection of motion of the body will be :

Options

A. `60^(@)`
B. `75^(@)`
C. `30^(@)`
D. `45^(@)`

Answer

To find the angle between the force and the direction of motion of the body, we can use the formula for work done:

\[ W = F \cdot d \cdot \cos(\theta) \]

where:
- \( W \) is the work done,
- \( F \) is the force applied,
- \( d \) is the displacement,
- \( \theta \) is the angle between the force and the direction of displacement.

### Step 1: Write down the known values
- Work done, \( W = 25 \, \text{J} \)
- Force, \( F = 5 \, \text{N} \)
- Displacement, \( d = 10 \, \text{m} \)

### Step 2: Substitute the known values into the work done formula
Using the formula:
\[ W = F \cdot d \cdot \cos(\theta) \]

Substituting the known values:
\[ 25 = 5 \cdot 10 \cdot \cos(\theta) \]

### Step 3: Simplify the equation
\[ 25 = 50 \cdot \cos(\theta) \]

### Step 4: Solve for \( \cos(\theta) \)
To isolate \( \cos(\theta) \), divide both sides by 50:
\[ \cos(\theta) = \frac{25}{50} \]
\[ \cos(\theta) = \frac{1}{2} \]

### Step 5: Find \( \theta \)
Now, we need to find the angle \( \theta \):
\[ \theta = \cos^{-1}\left(\frac{1}{2}\right) \]

From trigonometric values, we know:
\[ \theta = 60^\circ \]

### Conclusion
The angle between the force and the direction of motion of the body is \( 60^\circ \).

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