Question

Work done is zero when the angle between force and displacement is:

• A. \( 0^\circ \)
• B. \( 45^\circ \)
• C. \( 90^\circ \)
• D. \( 180^\circ \)

Hint:

Remember:
- \( \theta = 0^\circ \): Maximum positive work.
- \( \theta = 180^\circ \): Maximum negative work (e.g., friction).
- \( \theta = 90^\circ \): Zero work.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the condition under which the physical work done by a force is zero based on the direction of displacement.

Step 2: Key Formula or Approach:
Work done (\( W \)) is defined as the dot product of force (\( \mathbf{F} \)) and displacement (\( \mathbf{d} \)): \[ W = F \cdot d \cdot \cos(\theta) \] where \( \theta \) is the angle between the force and displacement vectors.

Step 3: Detailed Explanation:
For work done to be zero (\( W = 0 \)), either \( F=0 \), \( d=0 \), or \( \cos(\theta) = 0 \).
We know that \( \cos(90^\circ) = 0 \).
Therefore, when the force is applied perpendicular to the direction of displacement (\( \theta = 90^\circ \)), the work done is zero.
Examples include a person carrying a heavy load on their head while walking horizontally.

Step 4: Final Answer:
The work done is zero when the angle is \( 90^\circ \).