Tool and proper metric unit to measure the following..?

[GameAnger]

Indicate the tool and a proper metric unit you would use to measure the following items. No sentences needed. I just needed help with it because obviously you wouldn't measure the mass of the Earth in grams. Thanks!

a) mass of a nail

b) volume of a cup of water

c) distance from here to california

d) mass of a piece of dirt

e) density of a pebble

f) mass of the earth

[Function]

a) scale, grams

b) scale, kilograms (use density of water, substract glass mass)

c) Google Maps (don't know; what's "here"?), a car, perhaps, after resetting your kilometers counter?, kilometers

d) scale, grams

e) ok, now this is a bit more complicated: fill a glass (perfect cilinder, of which height and radius are known) with water. Calculate the volume of the water. Drop the pebble in the water, and recalculate the volume of the 'water'. Substract original volume of new volume, and you have the volume of the pebble. Weigh the pebble, using a scale, and use the mass and volume to calculate density.

f) can't measure it with equipment, for the earth is not supported. You could base yourself on the formula for gravitational force (g):

[math]g=G\cdot\frac{m}{r^2}[/math] with m = mass of the earth, r = radius of the earth and G = gravitational constant, approx. [math]6.67\cdot 10^{-11} \frac{m^3}{kg\cdot s^2}[/math] and g = approx. [math]9.81\frac{m}{s^2}[/math] and r = approx. 6.371 km. Just isolate m out of the formula, and you have the mass of the earth. Express result in kilograms or megaton, gigaton, whatever you prefer.

Edited September 8, 2013 by Function

[Ilex aquifolium]

This link mentions using a tool to measure the earth, I only skim read it because I was just trying to find something to demonstrate a vague recollection I had, so I hope it is useful. http://www.karlscalculus.org/measureearth.html