Question

When an object of mass 200g is submerged in methanol, its apparent weight is 1.052N. When submerged in benzene its apparent weight is 0.951N. If the density of methanol is 0.8g/cm^3, What is the density of benzene?​

Answer 1

The density of benzene can be calculated using the concept of apparent weight and Archimedes' principle. The density is approximately 0.888g/cm^3.

Step-by-step explanation:

To find the density of benzene, we can use the concept of apparent weight and Archimedes' principle. The apparent weight of an object submerged in a fluid is equal to its weight in air minus the buoyant force exerted on it by the fluid. The buoyant force is equal to the weight of the fluid displaced by the object. We can use the formula:

Apparent weight = Weight in air - Buoyant force

Given that the mass of the object is 200g and the apparent weight in methanol is 1.052N, we can find the weight in air. The weight in air is equal to the mass of the object multiplied by the acceleration due to gravity (9.8 m/s^2). After finding the weight in air, we can calculate the buoyant force in methanol using the density of methanol (0.8g/cm^3). We can then use the same process for benzene to find its density.

Using this method, we can conclude that the density of benzene is approximately 0.888g/cm^3.

Answer 2

When the object is submerged in methanol, it displaces an amount of methanol with weight 1.052 N, i.e. with mass = (1.052 N)/g ≈ 107.347 g. With a density of 0.8 g/cm³, this means the displaced methanol and hence the object itself have a volume of

v ≈ (107.347 g) / (0.8 g/cm³) ≈ 134.184 cm³

Likewise, when submerged in benzene, the object displaces 0.951 N of benzene, whose mass is (0.951 N)/g ≈ 97.041 g with the same volume as the object. So the density d of benzene is

d ≈ (97.041 g) / (134.184 cm³) ≈ 0.723 g/cm³