Question

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

Hint:

When calculating dimensions, always ensure that the units cancel out properly and match the given dimensions.

Answer 1

The modulus of elasticity \( E \) has dimensions \( [M L^{-1} T^{-2}] \), and torque has dimensions \( [M L^2 T^{-2}] \). Step 1: The modulus of elasticity per unit torque has dimensions: \[ \frac{[M L^{-1} T^{-2}]}{[M L^2 T^{-2}]} = [L^{-3}] \] Step 2: Now we compare this with the given dimension \( [M^a L^b T^c] \) and find that \( a = 0 \), \( b = -3 \), and \( c = 2 \). Final Conclusion: The value of \( c \) is 2, which corresponds to Option (3).