Question

You measure two quantities as A = 1.0 m ± 0.2 m, B = 2.0 m ± 0.2 m. We should report correct value for √AB as: (a) 1.4 m ± 0.4 m (b) 1.41m ± 0.15 m (c) 1.4m ± 0.3 m (d) 1.4m ± 0.2 m

Answer 1

Hola...

HERE IS THE ANSWER


so option d) is the right answer

Answer 2

Hey dear,

◆ Answer-
(d) √AB = 1.4 ± 0.2 m .

◆ Explaination-
# Given-
A = 1.0 m ± 0.2 m
B = 2.0 m ± 0.2 m

# Solution-
Average value of √AB -
x = √AB
x = √(1×2)
x = √2
x = 1.414
x = 1.4 m

Error in calculation of √AB -
∆x/x = 1/2 ∆A/A + 1/2 ∆B/B
∆x/x = 1/2 × 0.2/1 + 1/2 × 0.2/2
∆x/x = 0.1 + 0.05
∆x = 0.15 × x
∆x = 0.15 × 1.414
∆x = 0.2121
∆x = 0.2 m

Therefore, we should report √AB = 1.4 ± 0.2 m .

Hope this helps...