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. $[ M ]=[ T \, C^{-2} h ]$

Answer 1

Answer: (A)

$M \propto T^{x} v^{y} h^{z}$
$M' L^{0}T^{0} = \left(T'\right)^{x }\left(L^{1}T^{-1}\right)^{y} \left(M^{1}L^{2}T^{-1}\right)^{z}$
$M^{1}L^{0}T^{0} = M^{z} L^{y}+2^{z} + T^{x-y-z}$
$z = 1\quad\quad x - y - z = 0$
$y + 2z = 0\quad\quad x + 2 - 1 = 0$
$y = - 2\quad\quad x = - 1$
$M \Rightarrow T^{-1} C^{-2} h^{1}$