Question

A body is moved in a direction opposite to the direction of force acting on it. Work done is:
A. Against the force
B. Zero
C. Along the force
D. None of these

Answer 1

Hint: Work is a measurement of energy; it explains how much energy is consumed or released by a force over a distance. Work done can be either positive or negative, if the force has a component in the same direction as the displacement of the object, then the force is doing positive work. If the force has a component in the direction opposite to the displacement, the force does negative work.

Complete step by step answer:
We know that work is said to be done when force applied on an object shows the displacement in that object.
Mathematically we have,
\[W = \vec F.d\vec S = FdS\operatorname{Cos} \theta \]
Where,
$\vec F = $ Force applied.
$d\vec S = $ Displacement of an object.
$\theta = $ Angle between force applied and the displacement.
If the body is moved in a direction opposite to the force applied on it, then the work done is “Negative”.

I.e., the displacement is in the direction opposite to the force applied then angle between the force and displacement will be 180.
Thus,
$W = FdS\operatorname{Cos} 180 = - FdS$;
 $\because \operatorname{Cos} 180 = - 1$
Therefore, the work done is negative, i.e., against the direction of force.
Hence, option A is correct.

Note:
$F\operatorname{Cos} \theta $ is the magnitude of the $\vec F$ in the direction of $d\vec S$. $\operatorname{Cos} \theta $ explains about the relative direction of the force and displacement. If the component of force along the direction of the displacement is opposite in direction to the displacement then the sign of displacement vector and force vector will be different. This is regardless of which was chosen as a positive direction.