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 $
