Question:
The density of a cube is measured by measuring its mass and the length of its side. If the maximum errors in the measurement of mass and length are $4\%$ and $3\%$, respectively, then the maximum error in the measurement of the density is
The density of a cube is measured by measuring its mass and the length of its side. If the maximum errors in the measurement of mass and length are $4\%$ and $3\%$, respectively, then the maximum error in the measurement of the density is
Updated On: Jul 7, 2022
- $9\%$
- $13\%$
- $12\%$
- $7\%$
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The Correct Option is B
Solution and Explanation
Density $\left(\rho\right)=\frac{Mass}{Volume}=\frac{m}{l^{3}}$
$\frac{\Delta\rho}{\rho}\times100=\frac{\Delta m}{m}\times100+3 \frac{\Delta l}{l}\times100$
$=4\%+3\times3\%=13\%$
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Concepts Used:
Uncertainty in Measurement
- Atoms and molecules consist of very low mass. But they are present in huge numbers.
- Chemists have to deal with numbers as large as 602,200,000,000,000,000,000,000, which is the number of molecules of 2g of hydrogen.
- There are even other constants like the speed of light, charges on particles, Avogadro’s number and etc.
- To handle these large or small numbers, we use the following notation: m × 10n, which is, m times ten raised to the power of n. In this expression, n is an exponent having positive and negative values and m is that number that varies from 1.000… and 9.999…
- The scientific notation 573.672 can be written as 5.73672 × 102 and in the same way, 0.000089 can also be written as 8.9 × 10-5.
- All of these help us to attain easier handling, better precision, and accuracy while performing operations on numbers with high magnitudes.
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