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Q.

The energy of a system as a function of time t is given as Et=A2expαt , where α=0.2s1 . 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 Et at t=5s  is

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answer is 4.

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Detailed Solution

Energy of system is given as  Et=A2eαt
Taking natural log on both side gives
 lnE=lnA2+lneαt
 lnE=2lnAlnαt
Percentage error in measurement of E is given as
 ΔEE×100=2ΔAA×100+αΔt×100
 ΔEE×100=2×1.25+210×1.5×5
 ΔEE×100=2.25+1.5=4%
 

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