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Q.

A metal wire has mass 0.4±0.002g, radius 0.3±0.001mm, and length 5±0.02 cm. The maximum possible percentage error in the measurement of density will nearly be

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a

1.2%

b

1.6%

c

1.3%

d

1.4%

answer is D.

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Detailed Solution

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We know,  d=MV=Mπr2l

Proportional error,   Δdd=ΔMM+2Δrr+Δll

 =0.0020.4+2×0.0010.3+0.025 =0.024+0.023+0.025 =0.3+0.4+0.2460=0.9460 % error=0.9460×100=9460 ≈1.6%

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