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The energy of a system E(t) as a function of time is given as $E (t) = A^{2} \exp (- α t)$ , where $α = 0.2 s^{- 1}$ . The measurement of A has an error of 1.25%. If the error in the measurement of time is 1.50% then percentage error in the value of E(t) at t = 5s is :

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answer is B.

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Detailed Solution

Given,

$\begin{array}{l} E = A^{2} e^{- α t} \\ \Rightarrow \frac{d E}{E} = 2 (\frac{d A}{A}) - 0.2 (\frac{d t}{t}) t \\ \Rightarrow \frac{d E}{E} \times 100 = 2 (1.25) + 0.2 \times 5 \times 1.5 = 4 % \end{array}$

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