A) 5.0 ± 11%
B) 5.0 ± 6%
C) 5.0 ± 1%
D) 1.25 ± 5%
Correct Answer: A
Solution :
Let relative density be denoted by R, then \[R=\frac{{{w}_{air}}}{{{w}_{air}}-{{w}_{water}}}\] \[\Rightarrow \] \[R=\frac{{{w}_{air}}}{w}=5\] Error in w is \[0.05+0.05\] \[\Rightarrow \] \[\Delta w=0.10\,N\] \[\frac{\Delta R}{R}=\frac{\Delta {{w}_{air}}}{{{w}_{air}}}+\frac{\Delta w}{w}\] \[\Rightarrow \]\[\frac{\Delta R}{R}=\frac{0.05}{5}+\frac{0.1}{(5-4)}\] \[\Rightarrow \]\[\frac{\Delta R}{R}=0.01+0.1\] \[\Rightarrow \]\[\frac{\Delta R}{R}\times 100=11%\] So, \[R=5\pm 11%\]
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