Specific Gravity practice problem

[foxi]

"An object of 15 grams mass is immersed in a fluid of benzene, in which it suffers an apparent loss of 5 grams. Assuming the specific gravity of Benzene is .7, what is the specific gravity of the object?"

How do you go about this problem, and what the heck does "suffers an apparent loss..." mean?

Thanks!

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[Matugi]

Benzene's density must be 700 kg/m^3 according to the question stem.

Loss of apparent mass of 5 grams means that it "weighs" 10g in benzene. This means that the buoyant force caused by benzene is equal to that 5g loss in mass since forces must balance (15g downward weight force, 10g upward tension force from scale and 5g upward buoyant force).

Buoyant force = density * volume submerged * g
.05 N = 700 kg/m^3 * volume submerged * g
Volume submerged = volume of object = 7.14 * 10^-6 m^3

Now calculate the density of your object:
.015kg/7.14*10^-6 m^3 = 2100 kg/m^3

This means the object has a specific gravity of 2.1

Obviously my math may be off but I believe this is how you solve it

 

[theonlytycrane]

The weight of the object in the fluid is (.015 kg * 10 m/s^2) down. There's a buoyant force pushing the object up that makes the object feel like it's only (.010 kg * 10 m/s^2) which is the "suffers an apparent loss" part.

The buoyant force is also equal to density of the fluid * volume displaced * gravity. This lets you solve for volume displaced, and then calculate the density of the object. The specific gravity of the object is the ratio of the density of the object divided by the density of water.

 

[Wolfpack93]

The weight of the object in the fluid is (.015 kg * 10 m/s^2) down. There's a buoyant force pushing the object up that makes the object feel like it's only (.010 kg * 10 m/s^2) which is the "suffers an apparent loss" part.

The buoyant force is also equal to density of the fluid * volume displaced * gravity. This lets you solve for volume displaced, and then calculate the density of the object. The specific gravity of the object is the ratio of the density of the object divided by the density of water.

I think that you would need to divide by the density of benzene for the last step (assuming the question is asking about specific gravity with respect to benzene) but other than that that's right. From what I remember specific gravity doesn't have to be in reference to water just whatever fluid your object is placed in

 

[Online Teacher]

I will not go into any calculation but just try to explain the meaning of apparent loss. Let us consider this example. A body is weighed by suspending it from a spring balance and the reading shows 5 N (remember the spring balance gives weight but for our convenience the markings are given in kg). Now with one of your hand you gently push the body upwards keeping everything else the same then you will notice that the spring balance do not read 5 N any more. It will show a lower value say 4 N.What has happened? Has the mass of the body changed? Not possible. Then what is the reason for this apparent loss in weight? Reason is that you have given an upward force which is acting on the body and the balance shows the net force. This is the same what happens when you immerse a solid in liquid. It applies an upward force (which we call the upward thrust) and hence it appears as if the body has lost some weight. This is called the apparent loss because in real terms the weight does reduce but it appears so.