Consider two masses, one at A & other at D be placed arbitrarily.

Let

$I_3 =\text{Distance of mass placed at D from a,} \\\\ I_1 =\text{New mass movement of Inertia of the two masses,} \\\\ k_1 =\text{New radius of gyration,} \\\\ α=\text{Angular acceleration the body;} \\\\ I=\text{Mass moment of inertia of a dynamically equivalent system.} \\\\ k_\alpha =\text{Radius of gyration of a dynamically equivalent system.} \\\\ \text{We know that the torque required to accelerate the body,} \\\\ T=Iα=m(k_{\alpha})^2\alpha$

Similarly, the torque required to accelerate the two-mass system placed arbitrarily,

$T_1=I_1 \alpha=m(k_1)^2 \alpha$

Therefore, Difference between the torque required to accelerate the two-mass system and the torque required to accelerate the rigid body,

$T=m(k_1)^2-(K_{\alpha})^2 \alpha$

The difference of the torque T is known as correction couple. This couple must be applied when masses are placed arbitrarily to make the system dynamically equivalent.