A rigid body moves a distance of 10m along a straight line under the action of a force 5N. If the work done by this force on the body is 25 joules, the angle which the force makes with the force makes with the direction of motion of the body is:

Options

A. `0^(@)`
B. `30^(@)`
C. `60^(@)`
D. `90^(@)`

Answer

To find the angle that the force makes with the direction of motion of the body, we can use the work-energy principle. The work done by a force is given by the formula:

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

Where:
- \( W \) is the work done (in joules),
- \( F \) is the magnitude of the force (in newtons),
- \( s \) is the displacement (in meters),
- \( \theta \) is the angle between the force and the direction of displacement.

### Step-by-step Solution:

1. **Identify the given values:**
- Work done, \( W = 25 \, \text{J} \)
- Force, \( F = 5 \, \text{N} \)
- Displacement, \( s = 10 \, \text{m} \)

2. **Substitute the values into the work formula:**
\[ 25 = 5 \cdot 10 \cdot \cos(\theta) \]

3. **Calculate \( 5 \cdot 10 \):**
\[ 25 = 50 \cdot \cos(\theta) \]

4. **Rearrange the equation to solve for \( \cos(\theta) \):**
\[ \cos(\theta) = \frac{25}{50} \]

5. **Simplify \( \frac{25}{50} \):**
\[ \cos(\theta) = \frac{1}{2} \]

6. **Find the angle \( \theta \):**
\[ \theta = \cos^{-1}\left(\frac{1}{2}\right) \]
The angle whose cosine is \( \frac{1}{2} \) is \( 60^\circ \).

### Final Answer:
The angle \( \theta \) which the force makes with the direction of motion of the body is \( 60^\circ \).

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