Question

The length of a body is measured as 3.51 m, if the accuracy is 0.01mm, then the percentage error in the measurement is
a) 351%
b) 1%
c) 0.28%
d) 0.035%

Answer 1

The length of a body , L = 3.51 m
And accuracy of its length , ∆L = 0.01 mm = 0.01 × 10⁻³ m = 10⁻⁵ m
we know , % error = relative error × 100
or , % error in Length = ∆L/L × 100

Now, % error in Length = 10⁻⁵/3.51 × 100
= 10⁻³/3.51 = 1/3510
= 0.000284

I think question should be given accuracy 0.01m not 0.01mm
well, rule is the % error = relative error × 100

if ∆L = 0.01m and L = 3.51
Then, % error in measurement = 0.01/3.51 × 100 = 1/3.51 = 0.28 %

Answer 2

The length of a body , L = 3.51 m
And accuracy of its length , ∆L = 0.01 mm = 0.01 × 10⁻³ m = 10⁻⁵ m
we know , % error = relative error × 100
or , % error in Length = ∆L/L × 100

Now, % error in Length = 10⁻⁵/3.51 × 100
= 10⁻³/3.51 = 1/3510
= 0.000284

I think question should be given accuracy 0.01m not 0.01mm
well, rule is the % error = relative error × 100

if ∆L = 0.01m and L = 3.51
Then, % error in measurement = 0.01/3.51 × 100 = 1/3.51 = 0.28 %

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