Question

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

• A. $V^{-2}{A}^2{F}^2$
• B. $V^{-4}{A}^{2}F$
• C. $V^{-4}{A}^{-2}F$
• D. $V^{-2}{A}^2{F}^{-2}$

Answer 1

Answer: (B)

$\frac{F}{A}=y.\frac{\Delta \ell }{\ell }$
$\left[Y\right]=\frac{F}{A}$
$F=\frac{ML}{T^2}$
$L=\frac{F}{M}.T^2$
$L^2=\frac{F^2}{M^2}{\left(\frac{V}{A}\right)}^4\because T=\frac{V}{A}$
$L^2=\frac{F^2}{M^2{A}^2}\frac{v^4}{A^2}F=MA$
$L^2=\frac{V^2}{A^2}$
$\left[Y\right]=\frac{\left[F\right]}{\left[A\right]}=F^1{V}^{-4}{A}^2$