Question

The density of the mercury is $13600kg{{m}^{-3}}$. Its value in CGS system will be
A. $13.6gc{{m}^{-3}}$
B. $1360gc{{m}^{-3}}$
C. $136gc{{m}^{-3}}$
D. $1.36gc{{m}^{-3}}$

Answer 1

Hint: Write down the units of density in SI and CGS systems. Write the conversion factor for basic units for converting them from SI system to CGS system. With the use of this information now convert the unit of density and find out the equivalent value of density of mercury in the CGS system.

Complete step-by-step solution -
Units used to measure different quantities vary place to place. So to have a uniformity in units a system called ‘The International System of Units’ (abbreviated as SI) is used.
There are basic seven units defines in SI system:
1. Length - meter (m)
2. Time - second (s)
3. Amount of substance - mole (mole)
4. Electric current - ampere (A)
5. Temperature - kelvin (K)
6. Luminous intensity - candela (cd)
7. Mass - kilogram (kg)
CGS system is another metric system used for measurement of units. Following are some units in CGS system used in our daily life:
1. Length - centimetre (cm)
2. Time - second (s)
3. Temperature - kelvin (K)
4. Mass - gram (g)
Unit of density in SI system is $kg{{m}^{-3}}$
Therefore, Unit of density in CGS system will be $gc{{m}^{-3}}$
Conversion from SI system to CGS system:
1 meter = 100cm
1kg = 1000g
Therefore,
\[\begin{align}
  & 1\text{ }kg{{m}^{-3}}=1000\times {{100}^{-3}}gc{{m}^{-3}} \\
 & 1\text{ }kg{{m}^{-3}}={{10}^{-3}}gc{{m}^{-3}} \\
\end{align}\]
Therefore,
$\begin{align}
  & 13600kg{{m}^{-3}}=13600\times {{10}^{-3}}gc{{m}^{-3}} \\
 & 13600kg{{m}^{-3}}=13.6gc{{m}^{-3}} \\
\end{align}$
Thus, the value of mercury in the CGS system will be equal to $13.6gc{{m}^{-3}}$.
Hence, option (A) is correct.

Note: CGS system is a very commonly used system. But it does not contain units for all quantities. For example, the quantity like amount of substance has no unit in the CGS system. Some quantities such as time have the same unit in both SI and CGS systems. Basically CGS stands for Centimetre Gram Second. Centimetre, Gram and Second, these three are fundamental units. MKS stands for Kilogram Second System. Kilogram, Second and System are fundamental units of MKS. FPS stands for Foot Pound Second. Foot, Pound and Second are the fundamental units of FPS. So do not get confused between CGS, MKS and FPS.