MCQ
A sliver wire has mass $(0.6 \pm 0.006) \; g$, radius $(0.5 \pm 0.005) \; mm$ and length $(4 \pm 0.04) \; cm$. The maximum percentage error in the measurement of its density will be $......\,\%$
- ✓$4$
- B$3$
- C$6$
- D$7$
✓
Answer
Correct option: A.
$4$
a
$M=(0.6 \pm 0.006) \; g$
$M=(0.6 \pm 0.006) \; g$
$r=(0.5 \pm 0.005) \; mm$
$l=(4 \pm 0.04) \; cm$
$\rho=\frac{m}{V}$
$\Rightarrow \frac{\Delta \rho}{\rho}=\frac{\Delta m}{m}+\frac{2 \Delta r}{r}+\frac{\Delta l}{l}$
(Volume of cylinder $=\pi r^{2} l$ )
$=\frac{0.006}{0.6}+\frac{2 \times 0.005}{0.5}+\frac{0.04}{4}$
$100 \times \frac{\Delta \rho}{\rho}=4 \times 10^{-2} \times 100$
$\frac{\Delta \rho}{\rho} \times 100=4 \%$
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