Help finding center of mass of soda can? If you represent the soda can as a right-circular cylinder
radius=4 cm height =12 cm
We are told to neglect the mass of the can itself.
When the can is full the center of mass is at 6cm above the base, halfway along the axis of the can.
As the can is drained and air replaces the soda, the center of mass descends towards the bottom.
However when the can is completely empty the center of mass is still at 6cm.
Assuming the density of soda is 1 gram per cubic cm and the density of air is 0.001 grams per cubic cm.
Find the depth of soda in the can for which the center of mass is at it's lowest point.
I am not sure where to begin, I was trying to think of this as a linear case where the fulcrum is at a point with masses on either end, but I am extremely lost.
Thank you for the help