Question

If force $( F )$, length $( L )$ and time $( T )$ are taken as the fundamental quantities. Then what will be the dimension of density:

• A. $\left[ FL ^{-4} T ^{2}\right]$
• B. $\left[ FL ^{-3} T ^{2}\right]$
• C. $\left[ FL ^{-5} T ^{2}\right]$
• D. $\left[ FL ^{-3} T ^{3}\right]$

Answer 1

Answer: (A)

Density $=\left[ F ^{ a } L ^{ b } T ^{ c }\right] $
${\left[ ML ^{-3}\right]=\left[ M ^{ a } L ^{ a } T ^{-2 a } L ^{ b } T ^{ c }\right]}$
${\left[ M ^{1} L ^{-3}\right]=\left[ M ^{ a } L ^{ a + b } T ^{-2 a + c }\right]}$
$ a =1 ; a + b =-3 ; -2 a + c =0 $
$ 1+ b =-3 \,\,c =2 a $
$b =-4\,\, c =2$
So, density $=\left[ F ^{1} L ^{-4} T ^{2}\right]$