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Gravitational potential and Gravitational potential Energy – A doubt

I am very confused with the difference between U=GM/r which has a unit J/kg and U=GMm/r which is work done and have a unit of Joules. What are exactly their differences?

There’s a question “The gravitational potential difference between two points is 3.0×10^3 J/kg. Calculate the work done in moving mass of 4.0 kg between the two points.”

What I did was seeing their units and then equate since they’re J/kg and kg, I multiplied both magnitude which will give me ‘Joules’ in the end.

Like 3.0×10^3 J/kg = Workdone/4.0 kg

Please help, my print out book has some missing pages, which didn’t allow me to see the answer at the back of the book.

Posted by Taffs 

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Answer (Admin)

Gravitational potential difference is the work done per unit mass in carrying a body from one place to other.

 

Work done has the unit J and therefore the potential difference (i.e the work done per unit mass) should have the unit J/kg

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