Answer

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**Hint:**In order to solve above problem first write the formula of work done in terms of $\theta $ i.e.,

$W = FS\cos \theta $

Now use the concept that for maximum work done i.e., for maximum LHS, RHS also should be maximum.Hence, we will get a desired solution.

**Complete step by step answer:**

We know that if a body displaces by distance S on acting the force F, then work done by the force is

$W = FS\cos \theta $ …..(1)

Where $\theta $ is the angle between force F and displacement S.

Here, we have to calculate $\theta $ for maximum work done W. So, for maximum work done RHS of equation 1 will also be maximum.

We know that the maximum value of $\cos \theta $ is 1.

$\Rightarrow \cos \theta = 1$

$ \Rightarrow \cos \theta = \cos 0^\circ $

$ \therefore \theta = 0^\circ $

**Thus, displacement of the body must be in the same direction as that of force to get the maximum positive work.**

**Note:**In many problems, student may get confused between maximum and minimum values of $\sin \theta $ and $\cos \theta $ which are given as,

${(\cos \theta )_{\max }} = 1$ ${(\sin \theta )_{\max }} = 1$

${(\cos \theta )_{\min }} = - 1$ ${(\sin \theta )_{\min }} = 0$

And when $\theta $ is very small then,

$\sin \theta \approx \theta ,\cos \theta \approx 1$

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