If speed (V),acceleration (A) and force (F) are considered as fundamental units, the dimesnion of Young 's modulus will be :

Options

A. `FA^(2)V^(-4)`
B. `FA^(2)V^(-5)`
C. `FA^(2)V^(-3)`
D. `FA^(2)V^(-2)`

Answer

A

Explanation

Let `Y = [ V^(a) A^(b) F^( c )]`
` [ ML^(-1) T^(-2)] = [LT^(-1)]^(a) [LT^(-2)]^(b) [MLT^(-2)]^( c )`
` ML^(-1) T^(-2) = M^( c ) L^( a + b + c) T^( -a - 2b - 2 c )`
:. `c = 1 , a + b + c = -1 , -a - 2b - 2c = -2`
On solving , we get ` a = -4 , b = 2 , and c = 1`.