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# Ratio of the SI units to the 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: Learn about the Si units and CGS unit systems. Try to understand the definition of retardation and what it means. Find the units of retardation in both the system and take the ratio of the units.

Complete step by step solution:
Retardation can be defined as the opposite of acceleration. If a moving object is slowing down or its velocity is decreasing, the rate of change of velocity of the object is called the retardation.
The unit of retardation is the same as the unit of acceleration.
SI units or the International System of Units is a system of units based on the metre, kilogram, second, ampere, kelvin, candela and mole. This system has a set of prefixes to indicate multiplication or division by a power of 10.
CGS units or the centimetre-gram-second system is a system of units based on centimetre as the unit of length, gram as the unit of mass and second as the unit of time.
Now, in SI unit, the unit of retardation is $m{{s}^{-2}}$
In CGS unit, the unit of retardation is $cm{{s}^{-2}}$
The ratio of the SI unit and the CGS unit of retardation is given by,
$\dfrac{m{{s}^{-2}}}{cm{{s}^{-2}}}=\dfrac{m}{cm}$
Again, we can convert the unit from meter to centimetre as $1m=100cm$
So, the ratio will be,
$\dfrac{m}{cm}=\dfrac{100cm}{cm}=100={{10}^{2}}$
So, the correct option is (B)

Note: Retardation can also be called negative acceleration or deceleration. Units and dimensions of both retardation and acceleration are the same. The unit of both the quantities are $m{{s}^{-2}}$ and the dimensions of both the quantities are $\left[ {{M}^{0}}{{L}^{1}}{{T}^{-2}} \right]$.