I was solving one question in which girl on trolley of certain masses sits. Then certain force is applied on trolley which made some displacement. In my opinion work should be done by both Girl & Trolley. As force is applied on trolley(given) and on girl because she was sitting on that, it cause displacement also.but answer provided is that work done by girl is $0$.How come this please clear this misconception.
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Work is done on the girl - she experiences a force from the seat, and her kinetic energy will change.
However, to be fair that is an answer that depends on your frame of reference. If you look at it in the world frame of reference, then the girl is applying a force on the trolley, over the distance that the trolley is moving. This is equal and opposite to the work done by the trolley on the girl - resulting in kinetic energy of the girl increasing. In the trolley frame of reference, the girl's velocity does not change, and she does no work. In the world frame, I would say she is doing negative work on the trolley.
I hope that doesn't increase your confusion...
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$\begingroup$ Please explain how girl can apply $-ve$ work on trolley as she was just sitting on trolley( world frame of reference ) over a distance trolley moves. $\endgroup$– mnulbFeb 25, 2016 at 14:30
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1$\begingroup$ Conservation of energy. If the energy of the girl goes up (kinetic energy), then the energy of something else goes down (trolley, world). This means that the girl did negative work on the system, just as the system did positive work on the girl. In the world frame, the girl is moving just as the trolley is, so the force she applies to the trolley has an associated distance (namely, the distance that the trolley moved). If she had been walking along the trolley and pushed it, you would have no trouble seeing that she was doing work... but the force between her and trolley would be the same. $\endgroup$– FlorisFeb 25, 2016 at 14:34