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  • If speed V, area A and Force F are chosen as fundamental units, then the dimension of Young's modulus will be: Option: 1

If speed V, area A and Force F are chosen as fundamental units, then the dimension of Young's modulus will be:
Option: 1 FA^{2}V^{-1}
 
Option: 2 FA^{2}V^{-3}
 
Option: 3 FA^{2}V^{-2}  
Option: 4 FA^{-1}V^{0}

Answers (1)

best_answer

Let

\dpi{120} Y=F^{x} A^ y V^ \mathrm{z}
So

\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}=\left[\mathrm{MLT}^{-2}\right]^{\mathrm{x}}\left[\mathrm{L}^{2}\right]^{\mathrm{y}}\left[\mathrm{LT}^{-1}\right]^{\mathrm{z}}
\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}=[\mathrm{M}]^{\mathrm{x}}[\mathrm{L}]^{\mathrm{x}+2 \mathrm{y}+\mathrm{z}}[\mathrm{~T}]^{-2 \mathrm{x}-\mathrm{z}}

comparing the power of M and L and T

\\\mathrm{x}=1 \ldots(1)\\ x+2 y+\mathrm{z}=-1 \ldots . .(2)\\ -2 x-\mathrm{z}=-2 \ldots(3)

after solving

\\x=1 \\ y=-1 \\ \mathrm{z}=0 \\

Y=F A^{-1} V^{0}

Posted by

avinash.dongre

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