A spring with spring constant 35 N/m is attached to the ceiling, and a 5.5-cm-diameter, 1.3 kg metal cylinder is attached to its lower end. The cylinder is held so that the spring is neither stretched nor compressed, then a tank of water is placed underneath with the surface of the water just touching the bottom of the cylinder. When released, the cylinder will oscillate a few times but, damped by the water, quickly reach an equilibrium position. Requried:
When in equilibrium, what length of the cylinder is submerged?

Explanation:

Let length of cylinder submerged be L .

Upward force due to restoration force of spring = k L

= 35 L .

Buoyant force by water in upward direction = Vρg

V is volume of water displaced , ρ is density of water , g is acceleration due to gravity .

V = π R²L , R is radius of cylinder

V = 3.14 x (2.75 x 10⁻²)² x L

= 23.75 x 10⁻⁴ L

Buoyant force by water in upward direction =23.75 x 10⁻⁴ L X 1000 X 9.8

= 23.275L  N

Total upward force = 35 L + 23.275L  

= 58.275 L

For equilibrium ,

Total upward force = weight of cylinder

58.275 L = 1.3 x 9.8

L = .2186 m

= 21.86 cm

i just did an experiment like this in my science class. also the answer is yes, it will get separated because they are two opposites meaning if they are opposite they can not attract.

hope this .!