What is represented by the product of force with displacement in the direction of force?

Work

The correct answer is option 1. Work.

Work, in physics, is defined as the product of force and displacement in the direction of the force. Mathematically, it is represented as:

\[ \text{Work} = \text{Force} \times \text{Displacement} \times \cos(\theta) \]

Where:

Force is the magnitude of the force applied,

Displacement is the magnitude of the displacement of the object in the direction of the force,

\( \theta \) is the angle between the force vector and the displacement vector.

If the force and displacement are in the same direction (i.e., \( \theta = 0^\circ \)), then the work done is maximum. If the force and displacement are perpendicular to each other (i.e., \( \theta = 90^\circ \)), then the work done is zero.

Work is a scalar quantity and its SI unit is the joule (J). One joule is equal to one newton-meter (1 J = 1 N·m). Work can be positive, negative, or zero depending on the angle between the force and displacement vectors and the direction of force relative to the direction of displacement.