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4.2%
Explanation:
Given The density of cylindrical rod was measured by the formula ρ = 4m/πD^2l. The percentage errors in m, d, and l are 1%, 1.5%, and 0.5%. Calculate the % error in the calculated value of density.
We know that
Density ρ = 4m/πD^2l
Now we know that
Δρ/ρ max = Δm / m + 2ΔD/D + Δl/l
But given Δm/m = 1% ΔD/D = 1.5% and Δl / l = 0.5%
Therefore maximum percentage error in the calculated value of density will be
Δρ/ρ max = 1% + 2 x 1.5% + 0.5%
= 1 + 3 + 0.5
= 4.5%
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