Density

• The density of a substance is primarily determined by the mass of its individual atoms or molecules and how closely those particles are packed together. In solids, particles are usually tightly packed in a fixed structure, leading to higher densities compared to gases.

• Gases generally have much lower densities than solids or liquids because their particles are spread far apart with large amounts of empty space between them. For the same mass, a gas will occupy a significantly larger volume than its solid counterpart.

• Density is an intrinsic property, meaning it does not change based on the amount of the substance present. A small iron nail and a large iron anchor have the same density because they are made of the same material.

Measuring Regular Solids

• To determine the density of a regular shape (like a cube or sphere), first measure its mass using a digital balance. Then, use a ruler or calipers to measure its dimensions and calculate volume using geometric formulas such as $V = l \times w \times h$ for a cuboid.

Measuring Irregular Solids

• For objects with complex shapes, use the displacement method. Submerge the object in a displacement can (Eureka can) filled to the spout; the volume of water that overflows into a measuring cylinder is exactly equal to the volume of the object.

Measuring Liquids

• To find the density of a liquid, measure the mass of an empty graduated cylinder, add a known volume of the liquid, and measure the total mass. Subtract the empty cylinder's mass to find the liquid's mass, then divide by the observed volume.

• It is important to distinguish between the mass of an object (how much matter it contains) and its density (how concentrated that matter is).

• Unit Conversions: Always check if the question requires the answer in $kg/m^3$ or $g/cm^3$. To convert $g$ to $kg$, divide by $1000$; to convert $cm^3$ to $m^3$, divide by $1,000,000$.

• Precision and Errors: When reading a measuring cylinder, always look at the bottom of the meniscus at eye level to avoid parallax errors. This ensures the volume measurement is as accurate as possible.

• Sanity Checks: Remember that the density of water is approximately $1000 kg/m^3$ (or $1 g/cm^3$). If your calculated density for a metal is lower than this, or for a gas is higher, re-check your decimal places and conversions.