"In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of $\left[M^a L^b T^c\right]$. If $b=3$, the value of $c$ is _________."

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Given, measured quantity $= {{Modulus\,of\,elasticity} \over {torque}}$

$= {\sigma \over {\varepsilon \tau }} = {F \over {A\varepsilon \tau }}$ where, $\sigma$ = stress, $\varepsilon$ = strain, $\tau$ = torque

$= {F \over {A\varepsilon FL}}$

So, dimension $= {1 \over {[{L^2}][L]}}$ ($\varepsilon$ is dimensionless)

$= [{L^{ - 3}}] = [{M^0}{L^{ - 3}}{T^0}] = [{M^a}{L^b}{T^c}]$

$\Rightarrow c = 0$

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In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of $\left[M^a L^b T^c\right]$. If $b=3$, the value of $c$ is _________.

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In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of $\left[M^a L^b T^c\right]$. If $b=3$, the value of $c$ is _________.

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