Question

Will an object with a density of 1.05 g/ml float or sink in water? Explain

Answer 1

The density of water is very close to 1.0 gm/ml.
The object is more dense than water.
It will sink in water.

Answer 2

The object will sink, because it is more dense than water.

Let's see this in detail. There are two forces acting on the object:

- its weight, which points downward, given by

`W=mg=\rho_o V_o g`

where
`\rho_o` is the object's density,
`V_o` is its volume, and g is the gravitational acceleration.

- The buoyancy force, which points upward, given by

`B=\rho_w V_w g`

where
`\rho_w` is the water density,
`V_w` is the volume of water displaced by the object.

We see that it is always
`W>B`, so the object will sink. In fact:

`\rho_o > \rho_w`. We are told the object's density is 1.05 g/mL, while the water density is 1.00 g/mL.

`V_o \geq V_w`: the two volumes are equal when the object is completely submersed, and the volume of water displaced cannot be greater than the volume of the object.

So, W > B, and the object will sink.