A) \[2mg\,[1+{{(\eta /L)}^{2}}]\]
B) \[mg\,[1+{{(\eta /L)}^{2}}]\]
C) \[\frac{mg}{2}\,[1+{{(\eta /L)}^{2}}]\]
D) \[4mg\,[1+{{(\eta /L)}^{2}}]\]
Correct Answer: D
Solution :
For radioactive decay, we can write \[\frac{dN}{dt}\eta -\lambda N\] or \[\int\limits_{0}^{N}{\frac{dN}{\eta -\lambda N}}=\int\limits_{0}^{t}{dt}\] or, In \[\left( \frac{\eta -\lambda N}{\eta } \right)=-\lambda t\] or \[\frac{\eta -\lambda N}{\eta }={{e}^{-\lambda t}}\] or, \[N=\frac{\eta }{\lambda }[1-{{e}^{-\lambda t}}]\]
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