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If velocity (v), acceleration (a) and fo...

If velocity (v), acceleration (a) and force (F) are taken as fundamental quantities, the dimensions of Young's modulus (Y) would be

A

`V^(-4)A^2F`

B

`V^(-2)A^2 F^(-2)`

C

`V^(-4)A^2 F`

D

`V^(-2)A^2 F^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let Y = f (V,F,A)
`:. Y=KV^(x) F^(y) A^(z) , K rarr ` Unit less
`:. [Y] =[V]^(x) [F]^(y)[A]^(z)`
`:. [ML^(-1)T^(-2)] =[LT^(-1)]^(x)[MLT^(-2)][LT^(-2)]^(z)`
`:. [M][L^(-1)][T^(-2)]\=[M]^(y)[L^(x+y+z)][T^(-x-2y-2z)]`
`:. y =1 , x +y + z =-1 :.-x - 2y - 2z =2`
`:. x + z =-2 " " x + 2y + 2z =2`
`:. z = 2, x =-4 " " :. x + 2z = 0`
`:. [Y] =[V^(-4)FA^(-2)]`
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