A metal wire has mass (0.4 pm 0.002),g, radius (0.3 pm 0.001),mm and length (5 pm 0.02) ,cm. The maximum possible percentage error in the

Q: A metal wire has mass $(0.4 \pm 0.002)\,g$, radius $(0.3 \pm 0.001)\,mm$ and length $(5 \pm 0.02) \,cm$. The maximum possible percentage error in the measurement of density will nearly be $.......\%$

d $\rho=\frac{ M }{ V }$ $\rho =\frac{ M }{\pi r ^2 \ell}$ $\frac{\Delta \rho}{\rho} =\frac{\Delta M }{ M }+\frac{2 \Delta r }{ r }+\frac{\Delta l}{l}$ $\frac{\Delta \rho}{\rho} \%$ $=\left[\frac{0.002}{0.4}+\frac{2(0.001)}{(0.3)}+\frac{0.02}{5}\right] \times 100 \%$ $=\frac{1}{2} \%+\frac{2}{3} \%+\frac{2}{5} \%$ $=1.6 \%$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

A metal wire has mass $(0.4 \pm 0.002)\,g$, radius $(0.3 \pm 0.001)\,mm$ and length $(5 \pm 0.02) \,cm$. The maximum possible percentage error in the measurement of density will nearly be $.......\%$

A$1.4$
B$1.2$
C$1.3$
D$1.6$

NEET 2023, Easy

STD 11 Science
JEE
STD 11 - 1. units,dimensions and measurement
Physics

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