Question

if length L force F and time T are taken as fundamental quantities what would the dimensional equation of mass and densuty

Answer 1

If L, F and T are fundamental quantities then they’re related as

Unit of force = kg m/s²
[F] = [M L T⁻²] .....(1)

Dimensional equation of mass from equation (1) is
[M] = [F] / [L T⁻²]
[M] = [F L⁻¹ T²] .....(2)

Density = Mass / Volume

Dimensional equation of density is
d = [M] / [L³]
= [F L⁻¹ T²] / [L³] ......[∵ from equation (2)]
= [F L⁻⁴ T²]

Answer 2

mass (unit kg) = [M)]
F=MLT^-2=>M=FT^2L^-1
density(kgm^-1) =ML^-1
F=MLT^-2=>M=FT^2L^-1