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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 +-0.3 m`

D

`1.4 m+-0.2m`

Text Solution

Verified by Experts

The correct Answer is:
D
`"Given"," "A=1.0m+-0.2m, B=2.0m+-0.2m`
`"Let"," "Y=sqrt(AB)=sqrt((1.0)(2.0))=1.414 m `
Rounding off to two significant digit Y=1.4m
`(DeltaY)/Y=1/2[(DeltaA)/A+(DeltaB)/B]=1/2[(0.2)/(1.0)+(0.2)/(2.0)]=(0.6)/(2xx2.0)`
`Rightarrow " "DeltaY=(0.6Y)/(2xx2.0)=(0.6xx1.4)/(2xx2.0)=0.212`
Rounding off to one significant digit `DeltaY==0.2m`
Thus, correct value for `sqrt(AB)=r+Deltar=1.4+-0.2m`
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