When two magnetic poles of different pole strengths are placed at a distance of $3\mathrm{cm}$ from each other in the air, the effective force acting between them is $\frac{4}{3}\mathrm{CGS} \mathrm{units}$. Find the pole strength for both if their sum is $7\mathrm{CGS} \mathrm{units}$.

A hypothetical bar magnet $\left(AB\right)$ is cut into two equal parts. One part is kept over the other, so that pole $C_2$ is above $C_1$. If $M$ is the magnetic moment of the original magnet, what would be the magnetic moment of the combination, so formed?