What is work done when body will displaces perpendicular to the force ?

Options

A. (a)zero
B. (b)maximum
C. (c)minimum
D. (d)None of these

Answer

To solve the question "What is work done when a body displaces perpendicular to the force?", we will follow these steps:

### Step 1: Understand the Concept of Work Done
Work done (W) is defined as the dot product of force (F) and displacement (d). Mathematically, it is expressed as:
\[ W = \vec{F} \cdot \vec{d} \]
This means that work done is dependent on the angle between the force and the direction of displacement.

### Step 2: Analyze the Situation
In this case, the body is moving in a direction that is perpendicular to the applied force. Let's denote the displacement vector as \(\vec{d}\) and the force vector as \(\vec{F}\). If the angle between \(\vec{F}\) and \(\vec{d}\) is 90 degrees, we can use the formula for the dot product:
\[ W = |\vec{F}| |\vec{d}| \cos(\theta) \]
where \(\theta\) is the angle between the force and displacement vectors.

### Step 3: Determine the Angle
Since the force is applied perpendicular to the displacement, we have:
\[ \theta = 90^\circ \]

### Step 4: Calculate the Work Done
Using the cosine of 90 degrees:
\[ \cos(90^\circ) = 0 \]
Thus, substituting this into the work done equation:
\[ W = |\vec{F}| |\vec{d}| \cos(90^\circ) = |\vec{F}| |\vec{d}| \cdot 0 = 0 \]

### Step 5: Conclusion
Therefore, the work done when a body displaces perpendicular to the force is:
\[ W = 0 \]

### Final Answer
The work done is **0**.

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