Question

The density of brass on the CGS system is $8.4g/c{m^3}$. Its density in SI system is:
(A) $8.4kg/{m^3}$
(B) $84kg/{m^3}$
(C) $840kg/{m^3}$
(D) $8400kg/{m^3}$

Answer 1

SI unit of density is $kg/{m^3}$. So we have to convert $g/c{m^3}$ into $kg/{m^3}$and we know that: $1gm = {10^{ - 3}}kg$ $1gm = {10^{ - 3}}kg$ and
$1cm = {10^{ - 2}}m$.
With the use of these conversions we can find the density of brass in SI system.

Complete step by step solution:
SI unit is an international system of measurements that are used globally in technical and scientific research to avoid the confusion with the units. Standard unit system is important because it helps the world to understand the measurements in one set of unit systems.
The centimetre–gram–second system of units (CGS) is a variant of the metric system based on the centimetre as the unit of length, the gram as the unit of mass, and the second as the unit of time.
Here, the density of brass on the CGS system is $8.4g/c{m^3}$.
$\therefore$ $1gm = {10^{ - 3}}kg$
$\therefore$ $1cm = {10^{ - 2}}m$
$\therefore$ $8.4g/c{m^3}$ $=$ $\dfrac{{8.4 \times {{10}^{ - 3}}}}{{{{({{10}^{ - 2}})}^3}}}$ $kg/{m^3}$
$= 8.4 \times {10^{ - 3}} \times {10^6}$ $kg/{m^3}$
$= 8400$ $kg/{m^3}$
So, the density of brass on SI system is $8400$ $kg/{m^3}$.

Hence, the correct option is (D).

Note: There are $7$basic SI units.
1. Length – Meter
2. Mass – Kilogram
3. Time – Second
4. Electric current – Ampere
5. Thermodynamic temperature – Kelvin
6. Amount of substance – Mole
7. Luminous intensity - Candela