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A person measures two quantities as A = ...

A person measures two quantities as `A = 1.0 m +- 0.2 m ,B = 2.0 m +- 0.2 m` We should report correct value for `sqrt(AB)` as

A

`1.4 m +- 0.4 m`

B

`1.11 m +- 0.15 m`

C

`1.4 m +- 0.3 m`

D

`1.4 m +- 0.2 m`

Text Solution

Verified by Experts

The correct Answer is:
D
`sqrt(AB) = sqrt(2) = 1.4`
and error in `sqrt(AB)`
Let `Z = sqrt(AB)`
`(DeltaZ)/(Z) = 1/2 (DeltaA)/(A) + 1/2 (DeltaB)/(B)`
`(DeltaZ)/(1.4) = (1)/(2) ((0.2)/(1)) + 1/2 ((0.2)/(2))`
`(DeltaZ)/(1.4) = 0.1 + 0.05`
`DeltaZ = (0.15) (1.4) = 0.21`
`Z = (1.4 + 0.2)m`
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