Why Do Different Masses (and Weights) Fall at the Same Rate?
A quick answer is: As the value of g is the same for all falling objects (regardless of their mass) near the surface of the earth and in the absence of external forces, hence objects with different masses (and weights) fall together or fall at the same rate.
Downward acceleration g is the same for all – show with Newton’s Second Law of motion
Let’s get some more details now with the help of Newton’s Second Law of motion.
In about 1589, Galileo is reported to have dropped two balls having different masses, to disprove the claim that heavier (or more massive) balls should fall faster than lighter ones.
Galileo claimed that the two balls should accelerate downward at the same rate, due to Earth’s gravity.
Newton’s laws of motion explain why this is so.
For any object with mass m and weight W in free fall, its downward acceleration is g = W/m, according to Newton’s second law.
But weight is proportional to mass, so for any object, the ratio W/m is the same, making the downward acceleration g the same for all.
Near Earth’s surface g is about 9.8 m/s^2, though this varies slightly due to altitude and latitude.
In a vacuum, a penny and a feather fall with the same acceleration
The value of g is the same for all falling objects (regardless of their mass) near the surface of the earth and in the absence of external forces.
Air resistance, for example, would reduce the acceleration of falling until a terminal velocity (falling at constant velocity) is reached.
This is what happens to a feather when it is dropped along with a penny. Feather with a greater surface area faces air resistance more than the coin.
However, in many experiments, physicists can demonstrate that in a vacuum (where air resistance is absent), a penny and a feather fall with the same acceleration!