A body moves a distance of 20 m along a striaght line under the action of a force of 10N. If the work done is 100J, the angle between force and displacement vectors is

Options

A. `0^(@)`
B. `30^(@0`
C. `45^(@)`
D. `60^(@)`

Answer

To solve the problem, we need to find the angle between the force and displacement vectors given the work done, force, and displacement. We will use the formula for work done:

### Step-by-Step Solution:

1. **Understand the formula for work done**:
The work done (W) by a force (F) when it acts over a displacement (s) is given by the equation:
\[ W = F \cdot s \cdot \cos(\theta) \]
where \(\theta\) is the angle between the force vector and the displacement vector.

2. **Identify the given values**:
- Work done, \(W = 100 \, \text{J}\)
- Force, \(F = 10 \, \text{N}\)
- Displacement, \(s = 20 \, \text{m}\)

3. **Substitute the known values into the work done formula**:
\[ 100 = 10 \cdot 20 \cdot \cos(\theta) \]

4. **Calculate \(F \cdot s\)**:
\[ F \cdot s = 10 \cdot 20 = 200 \]
So, we can rewrite the equation as:
\[ 100 = 200 \cdot \cos(\theta) \]

5. **Solve for \(\cos(\theta)\)**:
\[ \cos(\theta) = \frac{100}{200} = \frac{1}{2} \]

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

### Final Answer:
The angle between the force and displacement vectors is \(60^\circ\).

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