Step 1: Dimensions of Modulus of Elasticity
Modulus of Elasticity (Young's Modulus) = StrainStress
Strain is dimensionless, so the dimension of Modulus of Elasticity = Dimension of Stress.
Stress = AreaForce=[L2][M1L1T−2]=[M1L−1T−2]
Step 2: Dimensions of Torque
Torque = Force×Distance
[M1L1T−2]×[L]=[M1L2T−2]
Step 3: Dimension of the Measured Quantity
The measured quantity is Modulus of Elasticity per unit Torque.
Dimension=[M1L2T−2][M1L−1T−2]=[M1−1L−1−2T−2+2]
=[M0L−3T0]=[L−3]
Step 4: Comparing with [MaLbTc]
Comparing the dimensions:
[M0L−3T0]=[MaLbTc]
a=0,b=−3,c=0
Step 5: Given b=3
Since we need to compare it with b=3, we take the magnitude of the value b=−3.
Therefore, the value of c is:
0