# What does it mean when "work done cannot be regained"?

This question came in the Rajshahi University admission exam in 2014-15

Q) Which one is true in the case of conservative force?

(A) Energy is wasted

(B) The work done cannot be regained

(C) The law of conservation of mechanical energy is not conserved

(D) None of the above

My interpretation of B

When we throw a ball vertically upwards and it comes back to us after some time, the total work done by the force of gravity on the ball is zero, so the force of gravity is a conservative force. When the ball is thrown upwards, then negative work is done on the ball by the force of gravity in the first half, and then positive work is done by the force of gravity on the ball: the work done is "regained".

On the contrary, when we move a box along a surface that has friction, no matter in which direction we push the box, the work done by the frictional force on the ball is negative. So, the work done is always negative in the case of non-conservative forces, unlike conservative forces. So, we can say that the work done cannot be regained.

(A) and (C) are clearly wrong. According to my explanation, (B) should also be wrong. So, (D) should be the correct answer.

However, the question bank says that the correct answer is (B). Why is it saying that?

• I also think the correct answer is D. Are you by any chance preparing for a competitive exam? The question banks are highly erroneous, especially in Indian books. Jul 2, 2022 at 13:52
• Can you give a reference? (Which "question bank"?) Jul 2, 2022 at 14:35
• @robphy This site has seen many questions from students confused by bad admissions-exam preparatory materials (1, 2, 3, 4, 5, 6). Jul 2, 2022 at 21:39

## 1 Answer

However, the question bank says that the correct answer is (B). Why is it saying that?

Perhaps because they are simply wrong.

The trouble is I'm not quite sure what their choices mean.

In choice (A), what do they mean by "wasted" energy? Perhaps they are referring to energy no longer available to do work (second law)? In any case no energy is "wasted" in the sense that no heat is generated when all the work involved is done by conservative forces. So choice (A) would seem wrong.

In choice (B) what do they mean by "regained"? In any case, for conservative forces the work going from point a to point b is the negative of the work going from point b to a, for a net work of zero. So it would seem that (B) is wrong.

Choice (C) simply doesn't make sense. It essentially says a law is not conserved (???). Perhaps they meant the law is not obeyed. In any case the law of conservation of energy applies regardless of the forces involved. So choice (C) is clearly wrong.

So it would seem only choice (D) would make sense. But that entails making sense of the other choices which, frankly, are terribly worded.

Hope this helps.

• It seems that answers a-c are badly worded equivalents of: This process is not reversible. Jul 2, 2022 at 19:36
• @SteveSaban I got the same sense Jul 2, 2022 at 19:40