Question

What is the ratio of cgs to mks unit of acceleration?
$\begin{align}
  & a)\dfrac{m}{cm} \\
 & b)\dfrac{m}{s} \\
 & c)\dfrac{cm}{s} \\
 & d)\dfrac{cm}{m} \\
\end{align}$

Answer 1

Hint: The centimeter gram second system, abbreviated as cgs system, is a variant of metric system based on centimeter as unit of length, gram as unit of mass and second as unit of time. Similarly, in the meter kilo second system, each term is based on each quantity. Write the acceleration unit in terms of cgs and mks, divide both the units, we will get the ratio.

Complete step by step answer:
Acceleration is the rate of change of velocity per time taken by the body. In cgs units, the unit of acceleration is given as $cm{{s}^{-2}}$ and in the mks system, it is given as $m{{s}^{-2}}$.
If we divide both the units, we get
\[\begin{align}
  & ratio=\dfrac{cm{{s}^{-2}}}{m{{s}^{-2}}} \\
 & ratio=\dfrac{cm}{m} \\
\end{align}\]

So, the correct answer is “Option D”.

Additional Information: The cgs unit was first proposed in the year 1832 by the German mathematician carl Fredrich gauss to base a system of absolute units on three fundamental units of length, mass and time. Gauss chose the unit of millimeter, milligram and second. Later, in the year 1873, a committee of British association for the advancement of science recommended the adoption of the centimeter gram and second as fundamental units. The mks unit of the system uses meter, kilogram and second as the fundamental units to measure quantities. This system served as the basis for the development of an international system of units, abbreviated as SI.

Note: Both the systems use seconds as their fundamental units to measure the time. We can’t measure the units for quantities like magnetism and matter etc. Using these cgs and mks systems. Therefore, the international system for units, called si unit of system, is used globally for all the units of quantities in the modern days.