Physical World Units and Measurements - Result Question 46
47. 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
(a) $7 %$
(b) $9 %$
(c) $12 %$
(d) $13 %$
[1996]
Show Answer
Answer:
Correct Answer: 47. (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 % $
