CBSE Class 11-science Answered
Please solve the following question:
The energy of a system as a function of time t...(Please find full question in image.)
Asked by kirthanps | 22 Nov, 2020, 12:27: PM
Expert Answer
Energy of system at time t , E(t) = A2 exp( -α t ) .................(1)
where α = 0.2 s-1 is constant
By taking logarithm on both side of eqn.(1) , we get , ln [ E(t) ] = 2 ln(A) - α t ............(2)
By differentiating eqn.(2) , we get , ( dE/E ) = 2 (dA/A) - α dt .............(3)
we are given that , (dA/A ) × 100 = 1.5 % , i.e., dA/A = 0.015 ................(4)
(dt/t) × 100 = 1.25 % , i.e., dt/t = 0.0125 ...................(5)
Hence from eqn.(3) , we get at t= 5 s, ( dE/E ) = 2 × 0.015 + 0.2 × ( .0125 *5 ) = 0.0425
( error is always added together , hence - α dt is considered as + α dt in above calculation.
We can consder error in time ±dt , hence -ve sign is considered for dt to get maximum error possible)
Hence percentage error in E at t= 5 s is 4.25 %
Answered by Thiyagarajan K | 22 Nov, 2020, 02:10: PM
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