Question

If velocity $[ V ]$, time $[ T ]$ and force $[ F ]$ are chosen as the base quantities, the dimensions of the mass will be:

• A. $\left[ FT ^{-1} V ^{-1}\right]$
• B. $\left[ FTV ^{-1}\right]$
• C. $\left[ FT ^{2} V \right]$
• D. $\left[ FVT ^{-1}\right]$

Answer 1

Answer: (B)

$[ M ]= K [ F ]^{ a }[ T ]^{ b }[ V ]^{ c }$
$\left[ M ^{1}\right]=\left[ M ^{1} L ^{1} T ^{-2}\right]^{ a }\left[ T ^{1}\right]^{ b }\left[ L ^{1} T ^{-1}\right]^{ c }$
$a =1, b =1, c =-1$
$\therefore [ M ]=\left[ FTV ^{-1}\right]$