Time (T), velocity (3) 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

Options

A. `[M]=[T^(-1)C^(-2)h]`
B. `[M]=[T^(-1)C^(2)h]`
C. `[M]=[T^(-1)C^(-2)h^(-1)]`
D. `[M]=[TC^(-2)h]`

Answer

A

Explanation

Let mass, related as `M prop T^(x))C^(y)h^(z)`
`M^(1)L^(0)T^(0)=(T.)^(x)(L^(1)T^(-1))^(y)(M^(1)L^(2)T^(-1))^(z)`
`M^(1)L^(0)T^(0)=M^(z)L^(y+2z)T^(x-y-z)`
`z=1`
`y+2z=0" "x-y-z=0`
`y=-2" "x=-1`
`M=[T^(-1)C^(-2)h]`