... (salt water) of relative density 1.02 what fraction of its volume will be submerged?
Answers (1)
Get a ruler in your hands. Measure things until you start to understand how a ruler works. Measure some stuff and figure out where the center is. Say you measure a book and it's 7/8" thick. You look at your ruler and see that every eighth is divided into two sixteenths, so obviously half of 7/8" is going to be 7/16". If you write that out you have 1/2 x 7/8 = 7/16. And you notice that 1/2 is divided into 2/4 and then into 4/8 and so on, so you can convert anything to anything by multiplying all the numbers on top and then all the numbers on bottom.
Other rulers are divided into 10 and 100 parts. But an inch is still an inch, so anything on one ruler can be translated to the other ruler. A half inch on one ruler is 5/10 or 50/100 on the other. An eighth inch is just 12.5 marks when you have 100 marks per inch. A metric ruler divides an inch into 25.4 parts, so a half inch would be 12.7 of those parts. Pretty simple, isn't it? Practice this a bit and people will think you went to wizard school.
A body floats higher in salt water because salt water is denser. A body floats by displacing and equal weight of fluid, so we have a proportion:
1/(3/4) = 1.02/X The density of water is 1 gram/cc and the given density of salt water is 1.02 gram/cc
Any time you have to divide by a fraction, invert and multiply. Always.
4/3 = 1.02/X Now multiply by X.
4X/3 = 1.02 Multiply by 3/4.
X = 0.765 This says MORE than 3/4 of the body is submerged, so that tells us that the math is all wet. (A pun there. Try to keep it fun.)
Start over: 1/(1/4) = 1.02/X This is the same math, but working with the amount exposed instead of the amount submerged.
X = 1/4 x 1.02 = 0.255 Now we have a little more than 1/4 exposed, which is what we expect from the theory.