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A cylindrical wire of mass ( 0 . 4 ± 0 . 01 ) g has length ( 8 ± 0 . 04 ) cm and radius ( 6 ± 0 . 03 ) mm . The maximum error in its density will be

Options

  1. A3 . 5 %
  2. B5 %
  3. C1 %
  4. D4 %

Correct answer

D. 4 %

Step-by-step solution

The formula to calculate the density of the material of the wire is given by ρ = M πR 2 L       . . . 1 Hence, the formula to calculate the percentage error in calculating the density of the material can be written as d ρ ρ × 100 = d M M + 2 d R R + d L L × 100       . . . 2 Substitute the values of the known parameters into equation (2) to calculate the required percentage error. = 0 . 01 0 . 4 + 2 × 0 . 03 6 + 0 . 04 8 × 100 = 4 %

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