Question

Time $\left(T\right)$ ,Velocity $\left(C\right)$ and angular momentum $\left(H\right)$ are chosen as fundamental quantities instead of mass, length and time. In terms of these, dimension of mass would be:

• A. $\left[M\right]=\left[T^{-1}{C}^{-2}{h}^{-1}\right]$
• B. $\left[M\right]=\left[T^{-1}{C}^{2}h\right]$
• C. $\left[M\right]=\left[T^{-1}{C}^{-2}h\right]$
• D. $\left[M\right]=\left[T{C}^{-2}h\right]$

Answer 1

Answer: (C)

$\left[M\right]=\left[T^{-1}{C}^{-2}h\right]$

$m=T^a{C}^b{h}^c$

In dimensions,

$\left[m\right]=\left[T^1{]}^a\right[l^1{T}^{-1}{]}^b[M^1{L}^2{T}^{-1}{]}^c$

$=\left[T^a\right]\left[L^b{\underset{–}{T}}^{-b}\right]\left[M^c{L}^{2c}{\underset{–}{T}}^{-c}\right]$

$\left[M^1\right]=\left[T^{a-b-c}\right]\left[L^{b+2c}\right]\left[M^c\right]$

$c=1$

$a-b-c=0$

$b+2c=0$

$b+2=0$

$b=-2$

$a+2-1=0$

$a+1=0$

$a=-1$

$\left[m\right]=\left[T^{-1}{C}^{-2}{h}^1\right]$