A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in the measurement of the distance and the time are e₁ and e₂ respectively, the percentage error i…

Question

A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in the measurement of the distance and the time are e₁ and e₂ respectively, the percentage error in the estimation of g is

Accepted Answer

(2) e₁+2e₂. Given: the body starts from rest, so s=1/2gt². g=(2s)/(t²) Idea: weight each fractional error by the magnitude of its exponent and add. (Δ g)/g=(Δ s)/s+2(Δ t)/t In percentages, (Δ g)/g×100=e₁+2e₂.

Step-by-step solution

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