A) \[\frac{1}{2\sqrt{2}}\]
B) \[\frac{1}{2}\]
C) 2
D) \[\frac{1}{4}\]
Correct Answer: B
Solution :
When magnet is divided into two equal parts, the magnetic dipole moment \[M=\]pole strength\[\times \frac{l}{2}=\frac{M}{2}\] (pole strength remains same) Also, the mass of magnet becomes half,\[ie,\] \[m=\frac{m}{2}\] Moment of inertia of magnet \[I=\frac{m{{l}^{2}}}{12}\] New moment of inertia \[I=\frac{1}{12}\left( \frac{m}{2} \right){{\left( \frac{l}{2} \right)}^{2}}=\frac{m{{l}^{2}}}{12\times 8}\] \[\therefore \] \[I=\frac{I}{8}\] Now \[T=2\pi \sqrt{\left( \frac{I}{MB} \right)}\] \[T=2\pi \sqrt{\left( \frac{I}{MB} \right)}=2\pi \sqrt{\left( \frac{I/8}{MB/2} \right)}\] \[\therefore \,\,\,\,\,\,\,\,\,T=\frac{T}{2}\,\Rightarrow \,\frac{T}{T}\,=\frac{1}{2}\]
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