Gravitation Part 1

Gravitational potential energy on the earth surface of a body
U=−‌

GmM

R

And at the height h from the earth surface the potential energy
Uh=−‌

GmM

R+h

=−‌

GmM

2R

[as h=R]
So the gain in the potential energy
∆U=Uh−U
‌∴∆U=‌

−GmM

2R

+‌

GmM

R

‌⇒∆U=‌

GmM

2R

Now ‌

GM

R2

=g;‌‌∴‌

GM

R

=gR
∴∆U=‌

1

2

mgR