Physical World Units And Measurements Ques 43
43. The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are $4 \%$ and $3 \%$ respectively, the maximum error in the measurement of density will be
[1996]
(a) $7 \%$
(b) $9 \%$
(c) $12 \%$
(d) $13 \%$
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Answer:
Correct Answer: 43.(d)
Solution:
- (d) As we know, density $=\frac{\text{ mass }}{\text{ volume }}$
Maximum error in the measurement of density
$ \begin{aligned} & \rho=\frac{M}{L^{3}} \\ & \therefore \frac{\Delta \rho}{\rho}=\frac{\Delta M}{M}+3 \frac{\Delta L}{L} \end{aligned} $
$\%$ error in density $=\% $ error in Mass +$3 (\% $ error in length)
$ =4+3(3)=13 \% $
BETA
