Magnetism and Matter

We know that the time period for an oscillating magnet is given by:$T=2\pi\sqrt{\frac{I}{M B_H}}$where:$M$ is the magnetic moment,$I$ is the moment of inertia, and$B_H$ is the horizontal component of the Earth's magnetic field.Given that the magnetic moment decreases by $19\%$, we can express the initial magnetic moment as $M_1=m$ and the reduced magnetic moment as:$M_2=m-\frac{19\times m}{100}=0.81m$From the equation for the time period, we derive:$\frac{T_1}{T_2}=\sqrt{\frac{M_2}{M_1}}$Substituting the values we have:$\frac{T_1}{T_2}=\sqrt{\frac{0.81m}{m}}=\sqrt{0.81}=\frac{9}{10}$Rearranging gives:$T_2=\frac{10}{9}T_1$This implies:$T_2=1.11T_1$So, the new time period $T_2$ is $T_1+0.11T_1$, which indicates that:The time period increases by $11\%$.