A) 100 s
B) 20 s
C) 10 s
D) 50 s
Correct Answer: B
Solution :
\[A={{A}_{0}}{{e}^{-\gamma t}}\] \[A=\frac{{{A}_{0}}}{2}\]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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