Physics And Measurement Question 37
Question: A wire has a mass $ 0.3\pm 0.003g $ , radius $ 0.5\pm 0.005mm $ and length $ 6\pm 0.06cm $ . The maximum percentage error in the measurement of its density is
[IIT (Screening) 2004]
Options:
A) 1
B) 2
C) 3
D) 4
Show Answer
Answer:
Correct Answer: D
Solution:
$ \because $ Density, $ \rho =\frac{M}{V}=\frac{M}{\pi r^{2}L} $
$ \Rightarrow \frac{\Delta \rho }{\rho }=\frac{\Delta M}{M}+2\frac{\Delta r}{r}+\frac{\Delta L}{L} $
$ =\frac{0.003}{0.3}+2\times \frac{0.005}{0.5}+\frac{0.06}{6} $
$ =0.01+0.02+0.01=0.04 $
$ \therefore $ Percentage error $ =\frac{\Delta \rho }{\rho }\times 100=0.04\times 100=4% $
