Physical World Units and Measurements - Result Question 46

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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

======= ####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

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/physical-world-units-and-measurements/physical-world-units-and-measurements—result-question-46.md (a) $7 %$

(b) $9 %$

(c) $12 %$

(d) $13 %$

[1996]

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Answer:

Correct Answer: 47. (d)

Solution:

  1. (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 % $