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Question: The C.G.S unit of speed is: (a). \(cm/g\) (b). \(m/s\) (c). \(m/g\) (d). \(cm/s\)...

The C.G.S unit of speed is:
(a). cm/gcm/g
(b). m/sm/s
(c). m/gm/g
(d). cm/scm/s

Explanation

Solution

Hint: We know that speed is given by the formula, speed=distancetime\text{speed=}\dfrac{\text{distance}}{\text{time}}. Now, using this formula we will find the unit of speed in the MKS unit system and then find its CGS unit by converting MKS to CGS system.

Formula used: speed=distancetime\text{speed=}\dfrac{\text{distance}}{\text{time}}

Complete step by step answer:
Before finding the CGS unit of speed we will understand what is CGS and MKS unit system and how to convert any MKS unit into CGS unit system.
MKS unit means all the units of the quantity are in terms of kilogram, meter and/or second.
CGS unit means all the units of the quantity are in terms of gram, centimeter and/or second.
Now, to convert MKS into CGS we have to convert kilogram into gram, meter into centimeter. So, now we will find the MKS unit of speed. We know that speed is given by the formula,
speed=distancetime\text{speed=}\dfrac{\text{distance}}{\text{time}}
Where, the unit of distance is meter, and time is in second so, substituting the units in the expression we will get,
speed=ms\text{speed=}\dfrac{m}{s}
Now, we will convert MKS into CGS and we will get,
speed=ms⇒speed=cms\text{speed=}\dfrac{m}{s}\Rightarrow \text{speed}=\dfrac{cm}{s}
Hence, we can say that the CGS unit of speed is cm/scm/s.
Thus, option (d) is the correct answer.

Note: Students might get confused while converting from MKS to CGS unit system and due to that might make mistakes in finding the answer. Another method to solve the problem is by the method of dimensional analysis in which we have to find the dimensions of speed as per CGS system and then compare it with the options to find the answer.