One of the two rectangular components of a force is 10 N and it makes an angle 60° with the force. The magnitude of the force is :

Options

A. 7.1 N
B. 14.1 N
C. 17.3 N
D. 20 N

Explanation

To find the magnitude of the force given one of its rectangular components, we can use the relationship between the force and its components. Here’s a step-by-step solution:

### Step 1: Understand the Components of the Force
Given that one of the rectangular components of the force is 10 N and it makes an angle of 60° with the force, we can denote the force as \( F \) and the component as \( F_x \), where \( F_x = 10 \, \text{N} \).

### Step 2: Use the Cosine of the Angle
The component of the force along the direction of the angle can be expressed using the cosine function:
\[ F_x = F \cos(60^\circ) \]

### Step 3: Substitute the Known Values
We know that \( F_x = 10 \, \text{N} \) and \( \cos(60^\circ) = \frac{1}{2} \). Substituting these values into the equation gives:
\[ 10 = F \cdot \frac{1}{2} \]

### Step 4: Solve for the Force \( F \)
To find \( F \), we can rearrange the equation:
\[ F = 10 \div \frac{1}{2} \]
This simplifies to:
\[ F = 10 \times 2 = 20 \, \text{N} \]

### Conclusion
The magnitude of the force is \( 20 \, \text{N} \).

### Final Answer
The correct option is \( 20 \, \text{N} \).

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