Consider the following statements. Work is not done, when:

(Consider the work done either by the gravitational force or by the man or the earth )

CONCEPT:

• Work is said to be done by a force when the body is displaced actually through some distance in the direction of the applied force.
• Since the body is being displaced in the direction of F, therefore work done by the force in displacing the body through a distance s is given by

\(W = \vec F \cdot \vec s\)

Or, W = Fs cos θ

• Thus work done by a force is equal to the scalar or dot product of the force and the displacement of the body.

EXPLANATION:

• When the man moves on a horizontal surface, then work done by gravity is zero since gravitational force acts perpendicular to the displacement i.e., θ = 90° 

⇒ W = Fs cos 90° = 0         [∵ cos 90° = 0]

• When the moon is revolving around the earth then the work done by the centripetal force is always zero because centripetal force acts along the radius of curvature and towards its center but the displacement of the body is along circumference (tangent) which is perpendicular to the radius and thus the angle between the centripetal force and displacement is 90°.

⇒ W = Fs cos 90° = 0         [∵ cos 90° = 0]

• When a man travels on a horizontal platform with a load on his head, work done against gravity by the man is zero since gravitational force acts perpendicular to the displacement i.e., θ = 90° 

⇒ W = Fs cos 90° = 0         [∵ cos 90° = 0

• Therefore the work done is zero in all the cases. Therefore option 4 is correct.