Answer: the density of the liquid is approximately 2499.2 kg/m³
Step-by-step explanation:
To find the density of the liquid, we can use Archimedes' principle, which states that the buoyant force experienced by an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
The weight of the body in air is given as 98 N, and the weight of the body submerged in the liquid is given as 66.64 N. The difference in weight between the two states represents the weight of the liquid displaced by the body.
Weight of the liquid displaced = Weight in air - Weight submerged = 98 N - 66.64 N = 31.36 N
Now, we can use the formula for density:
Density = (Weight of the liquid displaced) / (Volume of the liquid displaced)
Since the weight of the liquid displaced is 31.36 N and the density of the body is given as 2500 kg/m³, we can rearrange the formula to solve for the volume of the liquid displaced:
Volume of the liquid displaced = (Weight of the liquid displaced) / (Density of the body)
Volume of the liquid displaced = 31.36 N / 2500 kg/m³ = 0.012544 m³
Now, we can find the density of the liquid:
Density of the liquid = (Weight of the liquid displaced) / (Volume of the liquid displaced)
Density of the liquid = 31.36 N / 0.012544 m³ ≈ 2499.2 kg/m³