A quantity Q has dimensions [MᵃLᵇTᶜ]. If its numerical value changes by factor 8 when the units of mass, length and time are changed to 2, 1/2 and 4 times their old values respectively, then:
Options

Question

A quantity Q has dimensions [MᵃLᵇTᶜ]. If its numerical value changes by factor 8 when the units of mass, length and time are changed to 2, 1/2 and 4 times their old values respectively, then:

G1 Physics · Accepted Answer

Physical quantity Q = n[MᵃLᵇTᶜ]. New unit of Q is multiplied by k = 2ᵃ(1/2)ᵇ4ᶜ = 2ᵃ⁻ᵇ4ᶜ. Numerical value changes inversely: n′/n = 1/k = 8. Therefore k = 1/8, i.e. 2ᵃ⁻ᵇ4ᶜ = 1/8.