Question

When a force retards the motion of a body, the work done is :
(A) Zero
(B) Negative
(C) Positive
(D) Positive or negative depending upon the magnitude of force and displacement.

Answer 1

If the displacement is in a direction opposite to the force, the angle formed between force and displacement is 180⁰. The formula of work done has a component of force in the direction of displacement i.e. F cos Ɵ and cos 180⁰ = -1.

Complete step by step answer:
When a force retards the motion of a body i.e., it opposes its motion. In this case, the acceleration is negative (retardation). The direction of the force is in the opposite direction to that of acceleration. Work done is given by the formula W = FS cos Ɵ where Ɵ is the angle formed between force F and displacement S. As the force accelerates the motion i.e. the applied force is in the opposite direction as of motion . So, the angle between the force and displacement is 180 degrees as it forms a straight line from the geometrical point of view. W= FS cos 180⁰ which gives work done as W= -FS since the value of cos 180⁰ is -1. Thus, the work done is negative.