Work is done by the porter against the force of gravity.
Explanation
In physics, Work is defined as the product of the force applied and the displacement in the direction of that force. Mathematically, \( W = F \cdot d \cdot \cos\theta \), where \( \theta \) is the angle between the force vector and the displacement vector. Lifting an object involves applying a force to overcome the gravitational pull.
Option Analysis:
- Work is done by the porter against the force of gravity. is Correct: To lift the luggage, the porter applies an upward force equal to (or slightly greater than) the weight of the luggage. The displacement is also in the upward direction. Since the applied force and displacement are in the same direction (\( \theta = 0^\circ \)), the porter does positive work. This work is performed against the resistive force of gravity.
- No work is done because the displacement is vertical. is Incorrect: Work is zero only if displacement is zero or if the force is perpendicular to displacement (\( \theta = 90^\circ \)). Here, the displacement is vertical and parallel to the applied force, so work is definitely performed. (Work is zero when a porter walks horizontally with a load, not when lifting it).
- Work is done by gravity in the direction of displacement. is Incorrect: The force of gravity acts downwards, while the displacement is upwards. The angle between gravitational force and displacement is \( 180^\circ \). Therefore, work done by gravity is negative and acts opposite to the direction of displacement.
- The work done depends on the time taken to lift the luggage. is Incorrect: The work done in lifting a mass \( m \) to a height \( h \) is given by \( W = mgh \). This quantity depends on mass, gravity, and displacement, but is independent of time. The quantity that depends on time is Power (Power = Work/Time).
Key Takeaway:
Lifting an object requires work to be done against gravity. The work done is calculated as \( W = mgh \) and is a scalar quantity independent of the time taken to complete the action.