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You measure two quantities as A = 1.0 m ...

You measure 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+-0.04 m`

B

`1.41m +-0.2 m`

C

`1.4m+-0.2 m`

D

`1.4m+-0.2 m`

Text Solution

Verified by Experts

Given `A=(1+-0.2) m, B=(2+-0.2)m`
Let `Y= sqrt(AB)= sqrt((1.0)(2.0))=1.414 m`
Rounding off to two significant digit Y=1.4 m
`(DeltaY)/(Y)=(1)/(2)[(DeltaA)/(A)+(DeltaB)/(B)]=(1)/(2)[(0.2)/(1.0)+(0.2)/(2.0)]=(0.6)/(2xx2.0)`
`DeltaY=(0.6Y)/(2xx2.0)=(0.61xx1.4)/(2xx2.0)=0.212`
Rounding off to one significant digit `DeltaY=0.2 m`
Thus `sqrt(AB)=r+-Deltar=1.4+-0.2 m`
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