If force F, area A and density D are teken as the fundamental units, the representation of Young's modulus 'Y' will be

Options

A. `F^(-1) A^(-1) D^2`
B. `FA^(-2)D^(-2)`
C. `FA^(-1) D^(0)`
D. `FA^(-1)D`

Answer

C

Explanation

`[y] = [F^a A^b D^c]`
`[ML^(-1)T^(-2)] = [(MLT^(-2))^a (L^(2))^b (ML^(-3))^c]`
Equating power of M, L and T
`1 = a + c " " -1 = a + 2b - 3c`
`-2 = - 2a " " a = 1 , " " c = 0`
`b = -1`
`[y] = F A^(-1) D^0`