Correct Option
The correct option isIt is the same for all three paths.
Explanation
The gravitational force is a conservative force. A fundamental property of conservative forces is that the work done in moving an object between two points is path-independent. It depends solely on the initial and final positions of the object, not on the trajectory followed.
Analysis
- Work Done Formula: The work done by gravity is calculated using the formula \( W = mgh \), where:
- \( m \) is the mass of the object.
- \( g \) is the acceleration due to gravity.
- \( h \) is the vertical displacement (height difference) between the initial and final points.
- Path Independence: Since the object moves from point A to point B in all three scenarios (vertical, zigzag, and ramp), the vertical displacement \( h \) remains constant. Consequently, the work done by gravity is identical for all three paths.
- Role of Time: Work is defined as the product of force and displacement. It is a scalar quantity independent of the time taken to perform the action. While power depends on time, work does not. Therefore, It depends on the time taken in each path. is incorrect.
Key Takeaway: Work done by conservative forces (such as gravity and electrostatic force) depends only on the vertical height difference between the starting and ending points, regardless of the path length or shape.