Time T , velocity C and angular momentum h are chosen as fundamental quantities instead of mass, length and…

Time T, velocity C and angular momentum h are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be:
  1. M=T-1C-2h
  2. [M]=[T1C2h]
  3. M=T-1C-2h-1
  4. [M]=[TC2h]

Solution

MTxCyhz
M1L0T0=T1xL1T-1yM1L2T-1z
[M1 L0T0]=[Mz Ly+2zTx-y-z]]
z=1
y+2z=0 , x-y-z=0
solving
y=-2
and x=-1
M T-1 C-2 h1

Asked in: JEE Main 2017 (08 Apr Online)

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