A) \[1.4m\pm 0.4m\]
B) \[1.41m\pm 0.15m\]
C) \[1.4m\pm 0.3m\]
D) \[1.4m\pm 0.2m\]
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 \[X=1.4m=(r)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(Let)\] \[\frac{\Delta x}{x}=\frac{1}{2}\left[ \frac{\Delta A}{A}+\frac{\Delta B}{B} \right]=\frac{1}{2}\left[ \frac{0.2}{1.0}+\frac{0.2}{2.0} \right]=0.212\] 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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