Energy of a system as a function of time t is given as E(t)=A^2 exp (-α t) , where α=0.2 s ^{-1} .

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1.Units, Dimensions and Measurement

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

A

$1$

B

$2$

C

$3$

D

$4$

(IIT-2015)

Solution

$E(t)=A^2 e^{-\alpha t}$

$\Rightarrow d E=-\alpha A^2 e^{-\alpha t} d t+2 A d A e^{-\alpha t}$

Putting the values for maximum error,

$\Rightarrow \frac{ dE }{ E }=\frac{4}{100} \Rightarrow \% \text { error }=4$

Standard 11

Physics

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