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

Answer

To solve the problem step by step, we will use the formula for work done, which is given by:

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

Where:
- \( W \) is the work done (in joules),
- \( F \) is the force applied (in newtons),
- \( d \) is the distance moved (in meters),
- \( \theta \) is the angle between the force and the direction of motion.

### Step 1: Identify the given values
From the problem, we have:
- Work done, \( W = 25 \, \text{J} \)
- Force applied, \( F = 5 \, \text{N} \)
- Distance moved, \( d = 10 \, \text{m} \)

### Step 2: Substitute the known values into the work formula
Using the work formula:
\[ W = F \cdot d \cdot \cos(\theta) \]
We can substitute the known values:
\[ 25 = 5 \cdot 10 \cdot \cos(\theta) \]

### Step 3: Simplify the equation
Now 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 the angle \( \theta \)
Now, we need to find the angle \( \theta \) for which \( \cos(\theta) = \frac{1}{2} \). The angle that satisfies this is:
\[ \theta = 60^\circ \]

### Conclusion
Thus, the angle between the force and the direction of motion of the body is:
\[ \theta = 60^\circ \]