Two bar magnets oscillate in a horizontal plane in earth's magnetic...

Torque on a bar magnet kept in a magnetic field is given by $τ = MBsin\theta$.

Hence, for small oscillations the time period of bar magnets is given by,

$T = 2\pi\sqrt{\dfrac{I}{MB}} ⇒ M ∝ \dfrac{I}{{T}^{2}}$

$⇒ \dfrac{{M}_{1}}{{M}_{2}} = \dfrac{{I}_{1}}{{I}_{2}} \times {\left(\dfrac{{T}_{2}}{{T}_{1}}\right)}^{2}$

$⇒ \dfrac{{M}_{1}}{{M}_{2}} = \dfrac{3}{2} \times {\left(\dfrac{4}{3}\right)}^{2} = \dfrac{8}{3}$