Convert SI unit of angular momentum into CGS unit by dimensional analysis method. 

Asked by thakursonali2000 | 13th Sep, 2015, 01:28: PM

Expert Answer:

The SI unit of angular momentum is kgm2s-1.
 
Hence, its dimensional formula is [M L2 T-1]
 
Now, we consider its numerical value as 1 kgm2s-1
 
According to the dimensional analysis method, the numerical value from one system of unit to another is
 
n1 [U1] = n2 [U2]
 
Here, n1 is the numerical value in SI units that is n1 = 1
 
So, now we have according to dimensional analysis that
 
begin mathsize 14px style 1 left square bracket straight M subscript 1 superscript straight a space straight L subscript 1 superscript straight b space straight T subscript 1 superscript straight c right square bracket equals straight n subscript 2 space left square bracket straight M subscript 2 superscript straight a space straight L subscript 2 superscript straight b space straight T subscript 2 superscript straight c right square bracket 1 space left square bracket straight M subscript 1 superscript 1 space straight L subscript 1 superscript 2 space straight T subscript 1 superscript negative 1 end superscript right square bracket equals straight n subscript 2 space left square bracket straight M subscript 2 superscript 1 space straight L subscript 2 superscript 2 space straight T subscript 2 superscript negative 1 end superscript right square bracket Now comma space we space know space that straight M subscript 1 equals 1 space kg equals 10 cubed space straight g semicolon space straight M subscript 2 equals straight g straight L subscript 1 equals 1 space straight m equals 10 squared space cm semicolon space straight L subscript 2 equals 1 space cm straight T subscript 1 equals 1 space straight s semicolon space straight T subscript 2 equals 1 space straight s So comma space we space get straight n subscript 2 equals fraction numerator left square bracket straight M subscript 1 superscript 1 space straight L subscript 1 superscript 2 space straight T subscript 1 superscript negative 1 end superscript right square bracket over denominator space left square bracket straight M subscript 2 superscript 1 space straight L subscript 2 superscript 2 space straight T subscript 2 superscript negative 1 end superscript right square bracket end fraction equals fraction numerator left square bracket 10 cubed space straight g space cross times space 10 squared space cm space cross times space 1 space straight s right square bracket over denominator left square bracket 1 space straight g space cross times 1 space cm space cross times space 1 space straight s right square bracket end fraction equals 10 to the power of 5 therefore 1 space kg space straight m squared space straight s to the power of negative 1 end exponent space equals space straight n subscript 2 space straight g space cm squared space straight s to the power of negative 1 end exponent equals 10 to the power of 5 space straight g space cm squared space straight s to the power of negative 1 end exponent end style

Answered by Romal Bhansali | 13th Sep, 2015, 06:12: PM