Question

When a force retards the motion of a body, the work done by the force during retardation is
A. Zero
B. Negative
C. Positive
D. Positive or negative depending upon the magnitude of the force

Answer 1

This is a direct question. We will make use of the formula that relates the work done, force, displacement, and the angle of displacement to solve this problem. As the retardation represents the negative sign, thus, we will substitute this value in terms of the angle of displacement to find the sign of the retardation.
Formula used:
$W=FS\cos \theta$

Complete step-by-step solution
In the case of retardation, the work done by the force will be negative. The force that relates the work done, force, the displacement, and the angle of displacement is given as follows.
$W=FS\cos \theta$
Where W represents the work done, F represents the force applied, S represents the displacement, and cos of angle represents the angle of displacement.
As during the retardation, the angle of displacement will be$180{}^\circ$, so, we will substitute this value in the formula. So, we get,
$W=FS\cos 180{}^\circ$
Substitute value of the cos angle.

& W=FS(-1) \\\ & W=-FS \\\ \end{aligned}$$ The above equation represents the work done by the force. As the work is done equals the negative of the product of the force and displacement, thus, the work done by the force will be negative. $\therefore$ When a force retards the motion of a body, the work is done by the force during retardation is negative. **As the work is done by the force during retardation is negative, thus, option (B) is correct.** **Note:** The retardation itself represents the negative sign, as it takes place in the opposite direction. The force that relates the work done, force, displacement, and the angle of displacement should be known to solve this type of problem.