A) \[3.75\text{ }rad\text{ }{{s}^{-1}}\]
B) \[1.25\text{ }rad\text{ }{{s}^{-1}}\]
C) \[2.50\text{ }rad\text{ }{{s}^{-1}}\]
D) \[5.00\text{ }rad\text{ }{{s}^{-1}}\]
Correct Answer: B
Solution :
| \[A\rho gx={{F}_{restoring}}\] |
| \[\pi {{r}^{2}}\rho gx=n{{\omega }^{2}}x\] |
| \[\therefore \] \[\omega \sqrt{\frac{\pi {{r}^{2}}\rho g}{\rho v}}\] |
| \[=r\sqrt{\frac{\pi g}{v}}\] |
| \[=2.5\times {{10}^{-2}}\sqrt{\frac{3.14\times 10}{310\times {{10}^{-6}}}}\] |
| \[=2.5\times {{10}^{-2}}\times {{10}^{2}}\sqrt{10}\] |
| \[\omega =2.5\times \sqrt{10}\] |
| \[\therefore \] \[f=\frac{2.5\times \sqrt{10}}{2\pi }\] |
| \[=1.25.\] |
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