Question

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 :

• A. \([M] = [T^{-1} C^{-2} h]\)
• B. \([M] = [T^{-1} C^{2} h]\)
• C. \([M] = [T^{-1} C^{-2} h^{-1}]\)
• D. \([M] = [T C^{-2} h]\)

Hint:

Express h/C^2 in M, L, T: it equals MT, so M = h C^-2 T^-1.

Answer 1

The Correct Option is A

Dimensions: \([T] = T\), \([C] = LT^{-1}\), \([h] = ML^2T^{-1}\).
Consider \(\frac{h}{C^2} = \frac{ML^2T^{-1}}{L^2T^{-2}} = MT\).
Therefore \(M = \frac{h}{C^2 T} = [T^{-1} C^{-2} h]\).
Answer: (1) \([M] = [T^{-1} C^{-2} h]\)