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

Question

If force ( F ), length ( L ) and time ( T ) are taken as the fundamental quantities. Then what will be the dimension of density: (A) [ FL -4 T 2] (B) [ FL -3 T 2] (C) [ FL -5 T 2] (D) [ FL -3 T 3]

Tardigrade Admin · Accepted Answer

Density =[ F a L b T c ] [ ML -3]=[ M a L a T -2 a L b T c ] [ M 1 L -3]=[ M a L a + b T -2 a + c ] a =1 ; a + b =-3 ; -2 a + c =0 1+ b =-3 c =2 a b =-4 c =2 So, density =[ F 1 L -4 T 2]

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

$[F L^{- 4} T^{2}]$

$[F L^{- 3} T^{2}]$

$[F L^{- 5} T^{2}]$

$[F L^{- 3} T^{3}]$

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

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

[FL−4T2]

[FL−3T2]

[FL−5T2]

[FL−3T3]