is potential energy mgh, negative when a particle is displaced against gravity?

Answers (1)

No potential energy is not negative when you displace particle against gravitation. 

Take help of vectors for understanding this,

U = -\int_{ref}^{r} \vec F. d \vec r

Now if you are displacing particle against gravity that means you are taking particle in upward direction while the direction of g is in downward. So the dot product will give positive value equal to mgh.

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