You measure two quantities as A=1.0m `+-0.2m`, `B=2.0m+-0.2m`. We should report correct value for `sqrt(AB)` as

Options

A. 1.4m`+-`0.4m
B. 1.41`+-`0.15m
C. 1.4m`+`0.3m
D. 1.4m`+-`0.2m

Answer

D

Explanation

Given, `A=1.0m+-0.2m`,`B=2.0+-0.2m`
Let, `Y=sqrt(AB)=sqrt((1.0)(2.0)1.414m`
Rounding off to two significant digit `Y=1.4m`
(triangleY)/(Y)=(1)/(2)[(triangleA)/(A)+(triangleB)/(B)]`
`=(1)/(2)[(0.2)/(1.0)+(0.2)/(2.0)]=(0.6)/(2xx2.0)`
`impliestriangleY=(0.6Y)/(2xx2.0)=(0.6xx1.4)/(2xx2.0)=0.212`
Rounding off to one significant digit
`triangleY=0.2m`
Thus, correct value for
`sqrt(AB)=r+triangler=1.4+-0.2m`