A) 4 sec
B) 2 sec
C) 0.5 sec
D) 0.25 sec
Correct Answer: B
Solution :
\[T=2\pi \sqrt{\frac{I}{M{{B}_{H}}}}=4\sec \] When magnet is cut into two equal halves, then New magnetic moment \[{M}'=\frac{M}{2}\] New moment of inertia \[{I}'=\frac{\left( \text{w}/2 \right){{\left( l/2 \right)}^{2}}}{12}=\frac{1}{8}.\frac{\text{w}{{l}^{2}}}{12}\] Where w is the initial mass of the magnet But \[I=\frac{\text{w}{{l}^{2}}}{12};\ \ \therefore \ {I}'=\frac{I}{8}\] \[\therefore \] New time period \[{T}'=2\pi \sqrt{\frac{{{I}'}}{{M}'{{B}_{H}}}}\] \[=2\pi \sqrt{\frac{I/8}{\left( M/2 \right){{B}_{H}}}}=\frac{1}{2}2\pi \sqrt{\frac{I}{{{M}_{H}}}}\] \[=\frac{1}{2}\times T=\frac{1}{2}\times 4=2\sec \]
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