TS EAMCET 9-Sep-2020 Shift 1 Solved Paper

Let magnetic dipole moment of given magnet is M. Then, its oscillation time period is $T=2\pi \sqrt{\frac{I}{M B}} = 2 \text{s} ( , )$ given $I=$ where, $=\frac{\omega l^{2}}{12}$ moment of inertia $M=$ and $\frac{l}{3}$ magnetic dipole moment of magnet. When magnet is cut into 3 parts, each part length is $\frac{\omega}{3}$ and mass of each part will be $I' = \frac{\omega' l^{2}}{12} = \frac{\frac{\omega}{3} \times \frac{l^{2}}{9}}{12} = \frac{1}{27} \times I$ So, moment of inertia of each part will be $M' = \frac{M}{3}$ Also, magnetic dipole moment of each part will be $=I_{1}=3 \times \frac{1}{27} I = \frac{1}{9} I$ Now, when these parts are placed one over other with like poles together, Moment of inertia of combination $M_{1}=3 \times \frac{M}{3}=M$ Also, dipole moment of combination is $T = 2\pi \sqrt{\frac{I_{1}}{M_{1} B}} = 2\pi \sqrt{\frac{\frac{I}{9}}{M B}}$ Hence, time period of oscillation of combination is