Newtons law of gravitation says that acceleration due to gravity (g) for any given object is independent of mass of the object and is proportional to Mass of the body attracting it and the square distance from the center of two objects.

i.e.,  \(g=\frac{GM}{r^2}\) [ magnitude of acceleration due to gravity]

But still in everyday experience we observe that coins fall way faster than feathers and the reason is the upward acting air resistance. Air resistance depends upon the mass of the falling object, for objects like feather the resistance the net downward acting force reduces and hence feathers drop way slower. To demonstrate that this is the case, Galileo conducted an experiment where he dropped coin and feather inside vacuum in absence of air resistance and proved that acceleration due to gravity (the rate of falling toward earth) is independent of mass of the object and the everyday experience is due to presence of air resistance.

This was how experiment was conducted.

Required Materials

• Around three meters of transparent vacuum tube made up of any materials like plastic of glass.
• Two rubber stoppers to fit at each ends of the tube. One of the rubber tube should have a small hole on it.
• A coin and a feather
• vacuum pump to suck air out of the vacuum (use commonly available vacuum pump)
• Two hose clamps.
• And someone to help with the experiment.

Arrangements

• Align the vacuum tube vertically on a comfortable stand or support.
• Gently, insert rubber stopper the one without hole at the bottom end of the tube.
• Partially, insert the copper tube through other rubber stopper (the one with hole) and gently insert this rubber stopper into top end of the vacuum tube.
• secure the rubber stopper and vacuum tube with the clamps if necessary so that it doesn't fall or the air doesn't leak into the tube during the experiment.
• The final arrangement should look something like this. 
• 

To Do and Notice

Without sucking air out of the tube, invert and tube and let the objects fall. One can notice that coin falls much faster than feather which is our normal day to day observation. Now using vacuum pump, get all the air out of the pump and then invert it again. If you feel some how air is passing into the tube you can let vacuum pump attached and invert the tube. Notice that feather fall much faster than earlier. Actually is is falling at the same rate as coin does. (Coin doesn't fall slower, feather falls faster). 

Conclusion

So the conclusion is that in presence of air net force acting downward reduces for feather and hence falls slower than coin. But in absence of air resistance, net downward force is just equal to force due to gravity which is same for both coin and feather and hence they fall down at the same rate.