Question

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

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

Answer 1

Answer: (D)

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