Taking foce, length and time to be the fundamental quantities find the dimension of
a. density, b. pressure,
c. momentum and d. energy

Answer

(I) `FL^(-4)T^(2)` (II) `FL^(-2)` (III) `FT ` (IV) `FL`

Explanation

`ML^(-3)=[MLT^(-2)]^(a)[L]^(b)[T)^(c)`
`ML^(-3)=M^(a)L^(b+b)T^(-2a+c)`
On comparing dimensions
`a=1,b=-4, c=2`
[density] `=F^(1)L^(-4)T^(2)`
(II) `ML^(-1)T-2=M^(a)L^(a+b)T^(-2a+c)`
On comparing
`a=b, b=0, c=1`
[Pressure] `=FL^(-2)`
(III) `ML^(-1)=M^(a)L^(a+b)T^(-2a+c)`
On comparing dimensions
`a=1, b=0, c=1`
[Momentum] `=FT`
(Iv) `ML^(2)T^(-2)=M^(a)L^(a+b)T^(-2a+c)`
On comparing dimensions
`a=1, b=1, c=0`
[Energy]`=FL`