Question

Near the earth surface PE = mgh and PE = GMm/r is equal .Give an example and prove

Answer 1

@sidsiddhartha

Answer 2

@aryandecoolest

Answer 3

@Chineseboy15 @♪Chibiterasu @tHe_FiZiCx99

Answer 4

@Abhisar @abb0t @jhonyy9 @Preetha @esshotwired @Gabylovesyou

Answer 5

@wyattp17

Answer 6

@texaschic101

Answer 7

Recall that g = GM/Re^2 at a distance from earth.

Also U(Re) = -gmM/Re. Subbing these equations into each other you get

U(Re) = -mgRe.

For very small heights h above the earths surface where h<<Re

U(Re + h) = -gmM/(Re + h) is approximately equal to -mg(Re +h).

So, the change in potential energy of a falling mass would be

\[\Delta U = Uf - Ui\]

which is U = (-mgRe - (-mg(Re +h))

U = mgh

Hope this helps :)