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 ________

Modulus of Elasticity: \(E = \left[ML^{-1}T^{-2}\right]\)

Torque: \(\tau = \left[ML^2T^{-2}\right]\)

Dimension of \(\frac{E}{\tau}\): \(\frac{\left[ML^{-1}T^{-2}\right]}{\left[ML^2T^{-2}\right]} = \left[M^{1-1} L^{-1-2} T^{-2-(-2)}\right] = \left[M^0 L^{-3} T^0\right]\)

Comparing with \(\left[M^a L^b T^c\right]\): \(a=0, b=-3, c=0\)

Given \(b=-3\), the value of \(c\) is \(0\).