- #1

Faiq

- 348

- 16

## Homework Statement

Derive E=mgh from Newton's law of Gravitation where h is very small. (Use binomial expansion)

**2. The attempt at a solution**

[tex]E = \frac{GMm}{(r+h)^2}-\frac{GMm}{r^2} [/tex]

[tex]E = \frac{GMm}{r^2}(\frac{1}{(1+\frac{h}{r})^2}-1) [/tex]

[tex]E = \frac{GMm}{r^2}((1+\frac{h}{r})^{-2}-1) [/tex]

[tex]E = \frac{GMm}{r^2}(1+\frac{-2h}{r}-1) [/tex] Other powers of h/r becomes negligible for h<<r

[tex]E = \frac{GMm}{r^2}(\frac{-2h}{r}) [/tex]

Not sure where I went wrong or what to do next

Note:- I know this can be solved in a million other methods but I want the answer specifically from this method. I had a book which used this method and I can't remember how this method works out.