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# Ratio of the SI units to CGS units of retardation is $A.\,{{10}^{-2}}$$B.\,{{10}^{2}}$$C.\,10$$D.\,{{10}^{-1}}$

Last updated date: 06th Sep 2024
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Hint: The SI units and the CGS unit system should be known to solve this problem. The definition of the retardation should be known to derive the unit of this. The SI unit of the retardation should be known, as well as, the CGS unit of the retardation should be known.

Complete step by step solution:
Firstly, let us know the definition of retardation. The opposite of the acceleration, the deceleration, is also called the retardation. The decreasing velocity of the body/object is known as the retardation. Or, in other words, the rate of decrease in the velocity of a body is called the retardation.
The unit of the acceleration is the same as the unit of the retardation, as, both the physical quantities are the same but with the opposite direction.
Now, let us know about the unit systems, that is, the SI units and the CGS systems. SI units are also called the International System of units to define the units of the physical properties, only of the 7 quantities in terms of meter, kilogram, second, mole, kelvin, candela and ampere. Whereas, the CGS system defines the units of the physical properties using mainly three parameters, such as centimetre for length, gram for the weight and second for the time.
The SI unit of the retardation is $m{{s}^{-2}}$, in CGS system, the unit of the retardation is $cm{{s}^{-2}}$.
Now, we will compute the ratio of these units. So, we have,
$\dfrac{m{{s}^{-2}}}{cm{{s}^{-2}}}=\dfrac{m}{cm}$
Now substitute the value of the meter in terms of centimeter. We know that 1 meter equals 100 cm, so we will make use of the same value.
\begin{align} & \dfrac{m{{s}^{-2}}}{cm{{s}^{-2}}}=\dfrac{100cm}{cm} \\ & \Rightarrow \dfrac{m{{s}^{-2}}}{cm{{s}^{-2}}}=\dfrac{100}{1} \\ \end{align}
Therefore, the ratio of SI units to CGS units of retardation is 100.

So, the correct answer is “Option B”.

Note: Not only the definition of the retardation but also the definitions of the SI units and the CGS system should be known to solve this problem. In this question, in order to obtain the ratio, we have converted the unit from one system to the other, that is, from the meter to cm. Thus, even this conversation should be known.