A force of `1200 N` acting on a stone by means of a rope slides the stone through a distance of `10 m` in a direction inclined at `60^@` to the force. The work done by the force is

Options

A. `6000 sqrt(3) J`
B. 6000 J
C. 12000 J
D. 8000 J

Explanation

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

### Step 1: Understand the formula for work done
The work done (W) by a force is given by the formula:
\[ W = F \cdot d \cdot \cos(\theta) \]
where:
- \( F \) is the magnitude of the force,
- \( d \) is the distance moved in the direction of the force,
- \( \theta \) is the angle between the force and the direction of motion.

### Step 2: Identify the values given in the problem
From the problem, we have:
- \( F = 1200 \, \text{N} \) (the force applied),
- \( d = 10 \, \text{m} \) (the distance moved),
- \( \theta = 60^\circ \) (the angle between the force and the direction of motion).

### Step 3: Calculate \( \cos(\theta) \)
We need to find \( \cos(60^\circ) \):
\[ \cos(60^\circ) = \frac{1}{2} \]

### Step 4: Substitute the values into the work done formula
Now we can substitute the values into the work done formula:
\[ W = 1200 \, \text{N} \cdot 10 \, \text{m} \cdot \cos(60^\circ) \]
\[ W = 1200 \, \text{N} \cdot 10 \, \text{m} \cdot \frac{1}{2} \]

### Step 5: Perform the calculation
Now we can calculate:
\[ W = 1200 \cdot 10 \cdot \frac{1}{2} \]
\[ W = 12000 \cdot \frac{1}{2} \]
\[ W = 6000 \, \text{J} \]

### Step 6: Convert to kilojoules if necessary
Since \( 1 \, \text{kJ} = 1000 \, \text{J} \):
\[ W = 6 \, \text{kJ} \]

### Final Answer
The work done by the force is \( 6000 \, \text{J} \) or \( 6 \, \text{kJ} \).

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