Density, Relative Density, and Fluid Columns
Mass density is mass per unit volume, and relative density is the dimensionless ratio of a substance's density to the density of water at the stated reference condition.
Why this shows up in the exam
Finding the mass or volume of a liquid charge · Comparing materials in flotation problems · Converting specific gravity data into SI density
Learn the idea
Density converts between mass and volume, while relative density compares a material directly with water. Equal-looking volumes need not weigh equally: density tells how tightly mass is packed. In layered columns, the denser liquid contributes more pressure for the same vertical height.
🧠 Memory hook: Density is mass packed into each unit volume; always compare like units.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- rho = m/V — definition for a homogeneous sample, or average density when m and V describe the whole body
- relative density = rho/rho_water — dimensionless comparison using the same unit system and stated reference density
How to approach it
- 1Identify the mass and the matching occupied volume
- 2Convert all densities into one unit system
- 3Check whether the question needs material, average, or fluid density
Common slip-ups that cost marks
- •Treating relative density as a quantity with units
- •Mixing grams per cubic centimetre with kilograms per cubic metre
- •Using material density for a hollow body's full external volume
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A wire 1 m long and cross-sectional area 2 mm^2 extends by 1 mm under a 200 N load. Find Young modulus.
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