Question

an object weighs 40N in air , weighs 20N when submerged jn water and 30N submerged in a liquid of unknown density .what is the density of the liquid?​

Answer 1

The density of the liquid can be determined using Archimedes' principle, which relates the weight loss of the object when submerged to the weight of the fluid displaced. By comparing the weight loss in water to that in the unknown liquid, we find that the density of the unknown liquid is 500 kg/m³.

Step-by-step explanation:

To determine the density of the liquid, 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. The apparent weight loss of the object when submerged is due to this buoyant force. When the object is submerged in water, it appears to lose 40N - 20N = 20N of weight, which is the weight of the water displaced by the object. The density of water is approximately 1000 kg/m³, which means that the volume of water displaced is equivalent to 20N of weight.

When the object is submerged in the unknown liquid, it loses 40N - 30N = 10N of weight. This 10N represents the weight of the unknown liquid displaced. Since the volume of the object is constant, the weight of the liquid displaced in both cases should be proportional to their densities. Therefore, using the density of water as a reference, we can calculate the density of the unknown liquid as follows: (Density of unknown liquid) = (Density of water) * (Weight loss in unknown liquid / Weight loss in water) = 1000 kg/m³ * (10N / 20N) = 500 kg/m³.

Answer 2

502.51 kg/m^3

Step-by-step explanation:

Upthrust on object in water is 40 - 20 = 20 N

Upthrust is equal to the buoyancy forces given as

B = pgv

p is density of water 1000 kg/m^3

g = acceleration due to gravity 9.81 m/s^2

v is the volume of liquid displaced.

Therefore

B = 1000 x 9.81 x v

20 = 9810v

v = 2.038x10^-3 m^3

For Upthrust in unknown liquid, we have 40 - 30 = 10 N

Bouyancy force for the liquid will be

B = P x 9.81 x 2.038x10^-3

NB- the same volume of fluid will be displaced i.e 2.038x10^-3 m^3

Equating we have

10 = P x 9.81 x 2.038x10^-3

10 = 0.0199p

p = 10/0.0199 = 502.51 kg/m^3