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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Solution
$\frac{{{\rm{ modulus of elasticity }}}}{{{\rm{ Torque }}}} = \frac{{{\rm{ Stress }}}}{{{\rm{ strain }} \times {\rm{ torque }}}}$
$ = \frac{{[{\rm{ Force }}]}}{{[{\rm{ Area }}] \times [{\rm{ Force }} \times {\rm{ length }}]}}$ $= \frac{1}{{[{\rm{ Area }} \times {\rm{ length }}]}} = \left[ {{{\rm{L}}^{ - 3}}} \right]$
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