Grounding a conducting object
The sphere acts as a capacitor of value \$C\$ charged at a voltage \$V_0\$ = \$Q\over C\$ relative to ground. When you connect the resistor it will discharge towards zero (relative to ground) exponentially, at a rate dependent on the RC product. 

\$ v(t) = V_0 \cdot (1 - e^{-t/\tau})\$ where \$\tau = R \cdot C\$

For all practical purposes, it will reach "close enough" to zero within 5 or 10 time constants, so for a sphere the size of a baseball a few inches from the earth and a resistor of 10 Meg ohm (quite high), it will be effectively at the same potential within the blink of an eye. The voltage everywhere on the sphere will be the same since it's conductive and no current is flowing. 

Mathematically, though, (and ignoring charge quantization and thermal noise in the resistor and such like) it never quite gets there.