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Our physics sir made us write that gravitational potential energy is the work done in bringing a mass from infinity to a point without acceleration, but I am confused because if acceleration is $0$ it means that the external force is 0, and hence net work done should always be zero. Then how can potential energy be anything other than zero?

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...if acceleration is $0$ it means that the external force is $0$...

No. If acceleration is $0$ then net force is $0$.

...and hence net work done should always be zero.

Yes, in this scenario the net work is in fact $0$, since the net force is $0$. However, this means that there are (at least) two forces acting on the object in question: gravity $F_g$ and an external force $F_e$. These two forces must be equal and opposite.

This is a standard treatment/explanation of potential energy. We move the body with a constant velocity, as $F_g=-F_e$, and so the work done by the external force $W_e$ is equal to the negative of the work done by gravity $W_g$. By definition, the work done by gravity is also equal to the negative change in potential energy $\Delta U$. Finally, if we start "at infinity" where $U(\infty)=0$ and end at position $x$, then $\Delta U=U(x)-U(\infty)=U(x)$,

Therefore, we have $$W_e=-W_g=-(-\Delta U)=\Delta U=U(x)$$ So then we have what you stated at the beginning:

gravitational potential energy is the work done in bringing a unit mass from infinity to a point without acceleration.

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  • $\begingroup$ Regarding your edit on the question : gravitational potential is the gravitational potential energy per unit mass. $\endgroup$ – user249968 Jan 2 '20 at 13:42
  • $\begingroup$ @JohanLiebert Yes, it is. The OP seemed to be mixing up both, so it could have gone either way. I chose to go the potential energy route. $\endgroup$ – BioPhysicist Jan 2 '20 at 13:53

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