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

Options

A. `1.4m pm 0.4m`
B. `1.41m pm 0.15m`
C. `1.4m pm0.3m`
D. `1.4m pm0.2m`

Answer

D

Explanation

Given, `A = 1.0m pm 0.2m,B = 2.0m pm 0.2m`
Let, Y = `sqrt(AB) = sqrt((1.0)(2.0)) = 1.414m`
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)/(2 xx2.0)`
`implies DeltaY = (0.6 Y)/(2xx20) = (0.6 xx1.4)/(2 xx 2.0) = 0.212`
Rounding off to one significant digit `Delta Y = 0.2 m`
Thus, correct value for `sqrt(AB) = r+ Deltar = 1.4 pm 0.2 m`