Physics And Measurement Question 294

Question: You measure two quantities as $ A=1.0m\pm 0.2m $

$ B=2.0m\pm 0.2m $ . We should report correct value for $ \sqrt{AB} $ as

Options:

A) $ 1.4m\pm 0.4m $

B) $ 1.41m\pm 0.15m $

C) $ 1.4m\pm 0.3m $

D) $ 1.4m\pm 0.2m $

Show Answer

Answer:

Correct Answer: D

Solution:

[d] As given that, $ A=1.0m\pm 0.2m,B=2.0m\pm 0.2m $

So, $ X=\sqrt{AB}=\sqrt{(1.0)(2.0)}=1.414m $

Rounding off upto two significant digit $ X=1.4m=(r)(Let) $

$ \frac{\Delta x}{x}=\frac{1}{2}[ \frac{\Delta A}{A}+\frac{\Delta B}{B} ]=\frac{1}{2}[ \frac{0.2}{1.0}+\frac{0.2}{2.0} ]=0.212 $

Rounding off upto one significant digit $ \Delta x=0.2m=\Delta r(Let) $

So, correct value of $ \sqrt{AB}=r+\Delta r=(1.4\pm 0.2)m $



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