# Q & A: Gravitational and inertial mass

Q:
if there is a 100kg book and a 10kg book,they were dropped at the same time at the same place from a 5 storey high tower.they landed at the same time. why is so?
- yeh chi (age 12)
meridian primary school, singapore
A:
This is one of the most fascinating subjects in physics! The question: "Why is the gravitational mass of an object exactly equal to its inertial mass" has given rise to a great many interesting lines of investigation.

Here's what that means:

Newton's second law says F = m*a, where F is the sum of all the forces on an object, m is its mass, and a is its acceleration.

Newton also found out that F = m*g expresses the force gravity exerts on an object (there may be other forces, but when you drop something, these other forces are temporarily not playing a role. Air resistance gums things up a little bit, but let's ignore that for now). The quantity g is just 9.81 meters/sec^2 near the earth's surface, and it gets weaker as you go away from the earth.

If gravity's the only force on a book, then its acceleration is just g. The mass divides out! You can drop anything, and as long as you don't have air resistance, it will fall at the same rate as if you dropped anything else.

This is one consequence of Einstein's equivalence principle, that a gravitational field and an accelerated reference frame (think: standing in an elevator that starts going up -- you feel momentarily as if gravity is turned up in the room a bit) are indistinguishable. Then all objects should accelerate the same in a gravitational field. But I still cannot answer the "why" part of why this is so.

Tom

(published on 10/22/2007)