A) Be double
B) Increase by \[\sqrt{2}\] times
C) Decrease by \[\sqrt{2}\] times
D) Be half
Correct Answer: B
Solution :
\[k=\frac{3EI}{{{L}^{3}}}\] \[{{\omega }_{n}}=\sqrt{\frac{k}{m}}=\sqrt{\frac{3EI}{m{{L}^{3}}}}=\sqrt{\frac{3EIg}{W{{L}^{3}}}}\propto \sqrt{\frac{1}{W}}\] \[\frac{{{\omega }_{n2}}}{{{\omega }_{n1}}}=\sqrt{\frac{{{W}_{1}}}{{{W}_{2}}}}=\sqrt{2}\]
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