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if E=ml^2t^-2 and frequency= t^-1 and planks constant = ml^2t^-1 are taken as fundamental units then find length and mass

if E=ml^2t^-2 and frequency= t^-1 and planks constant = ml^2t^-1 are taken as fundamental units then find length and mass

Grade:11

1 Answers

Raksh
24 Points
5 years ago
calculating L.....
      [L]=[E]^a[frequecy]^b[plancks cont]^c
      [L]=[ML^2T^-2]^a [T^-1]^b[ML^2T^-1]^c
      [L]=[M]^a+0b+c[L]^2a+2c[T]^-2a-b-2c
   eqating dimensional powers.........
    [M]^0=[m]^a+0b+c
      0=a+b
      a=-b............(1)
     [L]=[L]^2a+2c
      1=2a+2c...........(2)
    [T]=[T]^-2a-b-2c
     1=-2a-b-2c
      as a=-b
      1=-2a+a-2c
       1=3a-2c........(3)
   from (2)and(3)
    2=5a
    a=2/5,b=-2/5,c=3/5.....unit of lenght=[E]^2/5[freq.]^-2/5[h]^3/5
similarly, mass can be derived

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