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Question
Measure of two quantities along with the precision of respective measuring instrument is A = 2.5 ms–1 ± 0.5 ms–1 B = 0.10 s ± 0.01 s. The value of A B will be ______.
Options
(0.25 ± 0.08) m
(0.25 ± 0.5) m
(0.25 ± 0.05) m
(0.25 ± 0.135) m
Solution
Measure of two quantities along with the precision of respective measuring instrument is A = 2.5 ms–1 ± 0.5 ms–1 B = 0.10 s ± 0.01 s. The value of A B will be (0.25 ± 0.08) m.
Explanation:
The resultant significant figure in multiplication and addition is equal to the minimal number of significant figures.
A = (2.5 ± 0.5) ms–1
B = (0.10 ± 0.01) s
X = AB = 2.5 × 0.10
= 0.25 m
`(Δx)/x = (ΔA)/A + (ΔB)/B`
`(Δx)/x = 0.5/2.5 + 0.01/0.10`
`(Δx)/x = 0.075/0.25`,
`Δx` = 0.007
≅ 0.08
∴ AB = (2.5 ± 0.08) m
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