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

Answer

(d)

Explanation

Here, `A = 1.0 m +- 0.2m, B = 2.0 +- 0.2m`
`x =sqrt(AB) = sqrt((1.0)(2.0)) = 1.414m.`
Rounding off to two significant digits, `x = sqrt(AB) = 1.4m.`
Now,`(Deltax)/(x) = (1)/(2)[(DeltaA)/(A) + (DeltaB)/(B)] = (1)/(2)[(0.2)/(1.0) + (0.2)/(2.0)] = (0.6)/(2xx2.0)`
`Deltax= (0.6x)/(2xx2.0) = 0.15xx1.414 = 0.2121`
Rounding off to one significant digits, `Deltax = 0.2 m`
Hence, `sqrt(AB) = 1.4m +- 0.2m`