The energy is E(t)=A²exp(−αt), with α=0.2 s⁻¹. A has 1.25% error and time has 1.50% error. At t=5 s, find the percentage error in E.
Physics · Unit dimension and error
JEE Advanced 2015

Question

The energy is E(t)=A²exp(−αt), with α=0.2 s⁻¹. A has 1.25% error and time has 1.50% error. At t=5 s, find the percentage error in E.

G1 Physics · Accepted Answer

For E=A²exp(−αt), maximum fractional error is ΔE/E = 2ΔA/A + αΔt. ΔA/A=1.25%; Δt=1.5% of 5 s=0.075 s. Hence percentage error=2.5+0.2×0.075×100=4%. Answer: 4.