Question 60 of 121
The energy of a system is given as , where t is the time and . The errors in the measurement of and are and , respectively. At , maximum percentage error in the energy is :
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Answer: (A)
$\begin{aligned}
& d E=3 \alpha^2 d \alpha e^{-\beta t}+\alpha^3 e^{-\beta t}(-\beta) d t \\
& \frac{d E}{E}=\frac{3 d \alpha}{\alpha}+(-\beta) d t \\
& \frac{\Delta E}{E}=\frac{3 \Delta \alpha}{\alpha}+\beta \Delta t
\end{aligned}$
(\%)
Putting values we get
& d E=3 \alpha^2 d \alpha e^{-\beta t}+\alpha^3 e^{-\beta t}(-\beta) d t \\
& \frac{d E}{E}=\frac{3 d \alpha}{\alpha}+(-\beta) d t \\
& \frac{\Delta E}{E}=\frac{3 \Delta \alpha}{\alpha}+\beta \Delta t
\end{aligned}$
(\%)
Putting values we get