Period of a Simple Pendulum with Varying Masses and Gravitational Forces

[rbwang1225]

Homework Statement

The usual formula for the period T of a simple pendulum of length l is T=2$\pi$$\sqrt{\frac{l}{g}}$ where g is the acceleration due to gravity. Denoting rhe inertial mass of the pendulum bob by m$_{i}$ and its gravitational mass by m$_{g}$, derive an alternative expression for T in terms of these masses, the radius R of the Earth and its mass M$_{g}$.

Homework Equations

The Attempt at a Solution

I just replaced g as $\frac{GM_{g} {m_{g}}}{R^{2}m_{i}}$.
I don't know if this is what the author wants.

 

[BruceW]

That looks correct to me.