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# PAT 2006 density question watch

1. Hi guys, can anyone explain to me why the density of the liquid is double the effective density of the cubes?
2. (Original post by Shaanv)
Why's liquid density = 2 x cube density?
Archimede's: Buoyant F = Cube's W
ρ_l(Vc/2)g = ρ_c*Vc*g => ρ_l = 2ρ_c
Note cubes of same ρ_c, different Vc
3. (Original post by Physics Enemy)
Archimede's: Buoyant F = Cube's W
ρ_l(Vc/2)g = ρ_c*Vc*g => ρ_l = 2ρ_c
Note cubes of same ρ_c, different Vc
Sorry i havent come across this before, i dont suppose u could dumb it down for me a little bit.

I figured that the buoyant force is equal to the weight of the object which is equal to the weight of the fluid displaced.

This is the part i am unsure of. As the cubes are only half submerged the cubes only displaced half their total volume of liquid.

As the mass of cubes equals mass of water displaced the density of the liquid must be double the effective density of the cubes so that the volume of liquid displaced is half the volume of the cubes. Thus half submerging them.

Does that make any sense? Sorry if im being stupid, i havent come accross this before.
4. (Original post by Shaanv)
weight of fluid displaced = buoyant force = cube's weight
Yes

(Original post by Shaanv)
Cube is half submerged, so volume of displaced liquid is half cube's volume.
Yes

(Original post by Shaanv)
...
Equal weight/mass in half the space means substance is twice as dense, as eqn shows.
5. (Original post by Physics Enemy)
Equal weight/mass in half the space means substance is twice as dense, as eqn shows.
So in terms of finding the volume of an irregular shape by submerging it in water, that is a specific case as water has a density of 1 g cm^-3?
6. (Original post by Shaanv)
In terms of finding volume of an irregular shape by submerging it in water, that's a specific case as ρ (water) = 1 gcm^-3?
If you want to do that, fill a container of water to the brim. Submerge the object, collect displaced water, measure volume (equals object's volume).

Or weigh displaced water, then V = M/ρ. Assumed object more dense than water i.e) fully submerges, else use less dense liquid.

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