A) 1.0 sec
B) 0.5 sec
C) 0.25 sec
D) 2.0 sec
Correct Answer: B
Solution :
\[T=2\pi \sqrt{\frac{I}{MB}}=2\pi \sqrt{\frac{\text{w}{{l}^{2}}/12}{\text{Pole}\ \text{strength}\times 2l\times B}}\] \[\therefore T\propto \sqrt{Wl}\] \[\therefore \,\frac{{{T}_{2}}}{{{T}_{1}}}=\sqrt{\frac{{{\text{w}}_{2}}}{{{\text{w}}_{1}}}\times \frac{{{l}_{2}}}{{{l}_{1}}}}=\sqrt{\frac{{{\text{w}}_{1}}/2}{{{\text{w}}_{1}}}\times \frac{{{l}_{1}}/2}{{{l}_{1}}}}=\frac{1}{2}\] \[\Rightarrow {{T}_{2}}=\frac{{{T}_{1}}}{2}=0.5\ s\]
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