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A force acts on a body and displaces it by a distance S in a direction at an angle θ with the direction of force. What should be the value of θ to get the maximum positive work ?

Answer
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Hint:In order to solve above problem first write the formula of work done in terms of θ i.e.,
W=FScosθ
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=FScosθ …..(1)
Where θ is the angle between force F and displacement S.
Here, we have to calculate θ 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 cosθ is 1.
cosθ=1
cosθ=cos0
θ=0

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 sinθ and cosθ which are given as,
(cosθ)max=1 (sinθ)max=1
(cosθ)min=1 (sinθ)min=0
And when θ is very small then,
sinθθ,cosθ1