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 0.4 m`
B. `1.41m pm 0.15 m`
C. `1.4m pm 0.3 m`
D. `1.4m pm 0.2 m`

Answer

D

Explanation

Given, `A=1.0m pm0.2m`
`B= 2.0m pm 0.2m`
Let `X= sqrt(AB)`
`=sqrt((1.0)^2(2.0))= sqrt(2.0)=1.414m`
`=1.4` (2 significant figures)
Relative error is
`(triangleX)/(X)=(1)/(2)(triangleA)/(A)+(1)/(2)(triangleB)/(B)`
`=(1)/(2)((triangleA)/(A)+(triangleB)/(B))`
`=(1)/(2)((0.2)/(1.0)+(0.2)/(2.0))`
`=(1)/(2)(0.2+0.1)=(0.3)/(2)=0.15`
`implies trianglex= 0.15X= 0.15xx1.414`
`=0.2121m= 0.2` (1 significant figures)
`X= 1.4 m pm 0.2 m`