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

Answer

D

Explanation

Given `A = 1.0m +- 0.2m, B= 2.0 m +- 0.2 m`
Let `V = sqrt(AB) = sqrt((1.0)(2.0)) = 1.414 m`
Rounding off to two significant digit `Y = 1.4m`
`(Delta Y)/(Y) = (1)/(2)[(Delta A)/(A) + (Delta B)/(B)]`
`= (1)/(2)[(0.2)/(1.0) + (0.2)/(2.0)] = (0.6)/(2 xx 2.0)`
`rArr Delta Y = (0.6Y)/(2 xx 2.0) = (0.6 xx 1.4)/(2 xx 2.0) = 0.20`
Rounding off to one significant digit Thus currect value for
`sqrt(AB) = r + Delta r = 1.4 +- 0.2m`