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 dimension of mass would be:

[M]=[TC⁻¹h]

[M]=[T⁻¹C⁻²h⁻¹]

[M]=[T⁻¹C⁻²h]

[M]=[T⁻¹C²h]

m=TaCbhc
In dimensions,
[m]=[T¹]a[L¹T⁻¹]b[ML²T⁻¹]c=[M¹]=[Tᵃ⁻ᵇ⁻ᶜ][Lᵇ⁺²ᶜ][Mᶜ]
c=1
a−b−c=0
b+2c=0
b+2=0
b=−2
a+2−1=0
a=−1
[m]=[T⁻¹C⁻²h¹]