Question

if the work done on a body by internal conservative force is negative then it's potential energy

Answer 1

yes you are absolutely correct

Answer 2

Well, to be more precise , it is said that change in potential energy is negative of work done

To prove it is actually simple. Just two laws are required.

Work energy theorem states,
Work Done, W= Change in Kinetic Energy
 = K.E. (final) - K.E. (initial)
 = Change in K.E .................................................(1)
Now, by Law of conservation of energy,
 Kinetic Energy + Potential Energy = Constant,
=>Change in K.E. + Change in P.E.=0
=> Change in K.E = - (Change in P.E.)
From Equation (1),
W = - (Change in P.E.)
=> Change in P.E. = - W
Hence, change in potential energy =-work done.

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