An object weighing 335 N in air is immersed in water after being tied to a string connected to a balance. The scale now reads 250 N. Immersed in oil, the object appears to weigh 290 N. (a) Find the density of the object. (b) Find the density of the oil.

(a.) Density of the object = 3.941 * 10³ kg/m³ = 3941 kg/m³

(b.) Density of oil = 529 kg/m³

Explanation:

Relative density = Density of a substance / density of water.

According to Archimedes's principal: It states that when a body is wholly or partly immersed in a liquid or fluid, it experience a loss in weight which is equal to the upthrust.

According to Archimedes's principal,

Relative density = weight in air (N) / Apparent loss of weight under water (N).

∴ Density of a object / Density of water = Weight of object in air/apparent loss of weight under water (Upthrust in water).

(a.)

where, Density of water = 1000kg/m³, weight of object in air = 335 N

Apparent loss of weight under water (upthrust in water) = 335 - 250 = 85N

∴ Density of the object = (weight of object in air/loss of weight under water) * density of water.

Density of the object = (335/85) * 1000 = 3.941 * 10³ kg/m³.

Density of the object = 3.941 * 10³ kg/m³.

(b.) Relative density of oil = Density of oil/Density of water.

From Archimedes's principal,

Relative density = Upthrust of the body in oil / Upthrust of the body in water.

Upthrust in oil = 335 - 290 = 45 N,

Upthrust in water = 85 N.,

Density of water = 1000 kg/m³

∴ Density of oil = (upthrust in oil / upthrust in water) * density of water

Density of oil = (45/85) * 1000 = 0.529 * 1000

Density of oil = 529 kg/m³