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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 pm 0.4 m`

B

`1.41 m pm 0.15 m`

C

`1.4 m pm 0.3 m`

D

`1.4 m pm 0.2 m`

Text Solution

Verified by Experts

The correct Answer is:
D
Given , A = 1.0 m `pm 0.2 `m, B=2.0 m `pm` 0.2 m
Let, Y=`sqrt(AB) = sqrt((10)(20))= 1.414 `m
Rounding off to two significiant digit Y= 1.4 m
`(DeltaY)/(Y) =1/2 [(DeltaA)/(DeltaA)+(DeltaB)/(B)] =1/2 [(0.2)/(1.0) +(0.2)/(2.0)] =(0.6)/(2x2.0)`
`implies DeltaY = (0.6Y)/(2xx2.0) =(0.6xx1.4)/(2xx2.0)=0.212`
Rounding off to one significant digit `DeltaY=0.2 m ` Thus, correct value for
`sqrt(AB) = r + Deltar = 1.4 pm 0.2 m`
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