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  • if we have time (T) velocity (c) and angular momentum (L) as the base quantities, then what will be the dimensions of mass?

  1. [M]=[T^-1 C^-2 H]
  2. [M]=[T^-1 C^2 H]
  3. [M]=[T^-1 C^-2 H^-1]
  4. [M]=[T C^-2 H]

Answers (1)

best_answer

Let 

m\propto t^{a}v^{b}L^{c}

where m - mass

t - time

v - velocity

L - angular momentum

dimension of mass = [M]

dimension of time = [T]

dimension of velocity [C] = [LT^{-1}]

dimension of angular Momentum  [H]=[ML^{2}T^{-1}]

[M]=[T]^{a}[C]^{b}[H]^{c}

\Rightarrow [M]=[T]^{a}[LT^{-1}]^{b}[ML^{2}T^{-1}]^{c}

power of T = 0 so, a-b-c=0

power of L =0 so, b+2c=0

power of M = 1 so, c =1

from these equations,

a = -1; b = -2, c=1

[M]=[T]^{-1}[C]^{-2}[H]

 

Posted by

Vishwash Tetarwal

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