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You measure two quantities as A=1.0m+-0....

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

A

`1.4m+-0.4m`

B

`1.41m+-0.15m`

C

`1.4m+-0.3m`

D

`1.4m+-0.2m`

Text Solution

Verified by Experts

The correct Answer is:
D
Here, `A=1.0+-0.2m,B=2.0m+-0.2m`
`AB=(1.0m)(2.0m)=2.0m^(2)`
`sqrt(AB)=sqrt(2.0)m=1.414m`
Rounding off to two significant figures, we get
`sqrt(AB)=1.4m`
`(Deltasqrt(AB))/(sqrt(AB))=(1)/(2)((DeltaA)/(A)+(DeltaB)/(B))=(1)/(2)((0.2)/(1.0)+(0.2)/(2.0))=(0.3)/(2)`
`Deltasqrt(AB)=(0.3)/(2)xxsqrt(AB)=(0.3)/(2)xx1.414=0.212m`
Rounding off to one significant figures, we get
`Deltasqrt(AB)=0.2m`
The correct value for `sqrt(AB)` is `1.4m+-0.2m`
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