If speed $V,$ area $A$ and force $F$ are chosen as fundamental units, then the dimension of Young's modulus will be :
A$FA ^{-1} V ^{0}$
B$FA ^{2} V ^{-1}$
C$FA ^{2} V ^{-3}$
D$FA ^{2} V ^{-2}$
JEE MAIN 2020, Diffcult
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A$FA ^{-1} V ^{0}$
a $Y = F ^{ x } A ^{ y } V ^{z}$
$M ^{1} L ^{-1} T ^{-2}=\left[ MLT ^{-2}\right] x \left[ L ^{2}\right] y \left[ L T ^{-1}\right]^{z}$
$M ^{1} L ^{1} T ^{-2}=[ M ]^{ x }[ L ]^{ x +2 y +z}[ T ]^{-2 x - z }$
comparing power of $ML$ and $T$
$x=1 \ldots(1)$
$x+2 y+z=-1$$...(2)$
$-2 x-z=-2$$...(3)$
after solving
$x=1$
$y=-1$
$z=0$
$Y=F A^{-1} V^{0}$
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