Question

SI unit of density is :

• A. Kg/cm$^3$
• B. Kg/m$^3$
• C. g/m$^3$
• D. g/cm$^3$

Hint:

Always refer to the base SI units for fundamental quantities (like mass in kg, length in m, time in s) to derive the SI units for derived quantities (like density, speed, force, etc.).

Answer 1

The Correct Option is B

Step 1: Define density.
Density is defined as mass per unit volume. Step 2: Recall the SI units for mass and volume.
In the International System of Units (SI):
The SI unit of mass is the kilogram (kg).
The SI unit of length is the meter (m).
The SI unit of volume, derived from length, is cubic meter (m$^3$). Step 3: Determine the SI unit of density.
Since density = mass / volume, the SI unit of density will be the SI unit of mass divided by the SI unit of volume.
SI unit of density = $\text{kilogram} / \text{cubic meter} = \text{kg/m}^3$. Step 4: Evaluate the given options.
(1) Kg/cm$^3$: This uses kilograms for mass, but cubic centimeters for volume, which is not the SI unit of volume.
(2) Kg/m$^3$: This uses kilograms for mass and cubic meters for volume, which are both SI units. This is the correct SI unit for density.
(3) g/m$^3$: This uses grams for mass, which is a common unit for mass but not the base SI unit (kilogram is).
(4) g/cm$^3$: This uses grams for mass and cubic centimeters for volume. Both are common units but not the primary SI units for density. (2) Kg/m$^3$