A) 100 s
B) 20 s
C) 10 s
D) 50 s
Correct Answer: B
Solution :
| [b] \[A={{A}_{0}}{{e}^{-\gamma t}}\] |
| \[A=\frac{{{A}_{0}}}{2}\]after 10 oscillations |
| \[\because \]After 2 seconds |
| \[\frac{{{A}_{0}}}{2}={{A}_{0}}{{e}^{-\gamma }}^{(2)}\] |
| \[2={{e}^{2\gamma }}\] |
| \[\ell n2=2\gamma \] |
| \[\gamma =\frac{\ell n2}{2}\] |
| \[\because \]\[A={{A}_{0}}{{e}^{-\gamma t}}\] |
| \[\ell n\frac{{{A}_{0}}}{A}=\gamma t\] |
| \[\ell n1000=\frac{\ell n2}{2}t\] |
| \[2\left( \frac{3\ell n10}{\ell n2} \right)=t\] |
| \[\frac{6\ell n10}{\ell n2}=t\] |
| \[t=19.931\sec \] |
| \[t\approx 20\sec \] |
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