Question

If force $F$, area $A$ and density $D$ are taken as the fundamental units, the representation of Young's modulus ${}^{\prime }{Y}^{\prime }$ will be

• A. $\left[F^{-1}{A}^{-1}{D}^{-1}\right]$
• B. $\left[F{A}^{-2}{D}^2\right]$
• C. $[F{A}^{-1}D]$
• D. $[F{A}^{-1}{D}^0]$

Answer 1

Answer: (D)

Young's modulus $=\frac{\text{ Stress }}{\text{ Strain }}=\left[M{L}^{-1}{T}^{-2}\right]$
$F\to \left[ML{T}^{-2}\right]$
$A\to \left[L^2\right]$
$D\to \left[M{L}^{-3}\right]$
$\left[M{L}^{-1}{T}^{-2}\right]={\left[ML{T}^{-2}\right]}^a{\left[L^2\right]}^b{\left[M{L}^{-3}\right]}^c$
$a+c=1,a+2b-3c=-1$
$\Rightarrow a=1-c\Rightarrow -2=-2a-3c$
$\Rightarrow 2=2a+3c$
$\Rightarrow 2=2-2c+3c$
$\Rightarrow 0=+c\Rightarrow c=0$
$\therefore a=1$
$1+2b=-1$
$2b=-2$
$\Rightarrow b=-1$
Young's modulus $=\left[F{A}^{-1}{D}^0\right]$