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. `1.4"m"pm0.4"m"`
B. `1.41"m"pm0.15"m"`
C. `1.4"m"pm0.3"m"`
D. `1.4"m"pm0.2"m"`

Answer

D

Explanation

Given, `A=1.0" m"pm0.2" m",B=2.0" m"pm0.2" 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)`
`rArr" "(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=1.4pm0.2`m