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) 1.41 m ± 0.15 m(c) 1.4 m ± 0.3 m (d) 1.4 m ± 0.2 m

Answer 1

Answer:

D) 1.4 m ± 0.2 m

Explanation:

A = 1.0 m ± 0.2m (Given)

B = 2.0 m ± 0.2m (Given)

Average value of √AB -

x = √AB

x = √(1×2)

x = √2

x = 1.414 or 1.4m

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 or 0.2m

Therefore, the correct value for √AB is 1.4 ± 0.2m.