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. If the maximum percentage errors in measurement of distance and time are e₁ and e₂ respectively, the percentage error in the estimation of g is:
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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. If the maximum percentage errors in measurement of distance and time are e₁ and e₂ respectively, the percentage error in the estimation of g is:

Options

G1 Physics · Accepted Answer

Step 1: For free fall h=½gt², so g=2h/t². Step 2: Therefore maximum fractional error is Δg/g = Δh/h + 2Δt/t. Step 3: Hence percentage error = e₁+2e₂. Final: Correct answer: B.