An object floats in a liquid of density 1.2×10 kg/m3 with one quarter of its volume above the liquid surface. You are required to determine the density of the object

750kg m

36 To determine the density of the object, we can use Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

Here's how you can use this principle to find the density of the object:

1. Determine the buoyant force on the object:
- The buoyant force (F_b) is equal to the weight of the liquid displaced by the object.
- The volume of the liquid displaced by the object is three-quarters of its total volume, since one quarter of its volume is above the liquid surface.
- The weight of the liquid displaced (W_displaced) is given by the formula W_displaced = density of liquid * volume of liquid displaced * gravity.

2. Calculate the weight of the object:
- The weight of the object (W_object) is given by the formula W_object = density of object * volume of object * gravity.

3. Apply Archimedes' principle:
- According to the principle, the buoyant force (F_b) is equal to the weight of the object (W_object).
- Therefore, F_b = W_object.
- Equating the formulas we derived earlier, we get: density of liquid * volume of liquid displaced * gravity = density of object * volume of object * gravity.

4. Solve for the density of the object:
- Rearrange the equation obtained in step 3 to solve for density of object: density of object = (density of liquid * volume of liquid displaced) / volume of object.

5. Substitute the values given in the problem:
- The density of the liquid is given as 1.2×10 kg/m3.
- The volume of the liquid displaced is three-quarters of the total volume of the object.
- Since the object is floating, its weight is equal to the buoyant force, which is equal to the weight of the liquid displaced.

After substituting these values into the formula from step 4, you will be able to calculate the density of the object.