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The density of a sphere is measured by measuring the mass and diameter. If it is known that the maximum percentage errors in the measurement of mass and diameter are 2 % and 3 % respectively then the maximum percentage error in the measurement of density is

Correct answer

11

Step-by-step solution

The density can be computed by ρ = m v = m πd 3 6 or ρ   ∝   m d 3 ∴ ∆ ρ ρ × 100 % = ∆ m m × 100 %   +   3 ∆ d d × 100 % or ∆ ρ ρ × 100 = 2 + 3 × 3 = 11 Hence, the percentage error in measurement of density is 11 %

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