Question:
If the errors involved in the measurement of a side and the mass of a cube are \(2\%\) and \(4\%\) respectively, the maximum permissible error in the density of the material is
If the errors involved in the measurement of a side and the mass of a cube are \(2\%\) and \(4\%\) respectively, the maximum permissible error in the density of the material is
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Density is mass divided by the cube of the side, so the percentage errors add with the side error counted three times.
Updated On: Nov 12, 2026
- \(2\%\)
- \(6\%\)
- \(10\%\)
- \(12\%\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept
Density of a cube of side \(a\) and mass \(m\) is \(\rho=\dfrac{m}{a^{3}}\). In a quotient or power, the maximum percentage errors add, and a power multiplies the error.
Step 2: Maximum relative error
\(\dfrac{\Delta\rho}{\rho}=\dfrac{\Delta m}{m}+3\dfrac{\Delta a}{a}\)
Step 3: Calculation
\(\dfrac{\Delta\rho}{\rho}\times100=4\%+3(2\%)=4\%+6\%=10\%\)
Final Answer:
The maximum permissible error in the density is 10%. \[ \boxed{\text{(C) }10\%} \]
Density of a cube of side \(a\) and mass \(m\) is \(\rho=\dfrac{m}{a^{3}}\). In a quotient or power, the maximum percentage errors add, and a power multiplies the error.
Step 2: Maximum relative error
\(\dfrac{\Delta\rho}{\rho}=\dfrac{\Delta m}{m}+3\dfrac{\Delta a}{a}\)
Step 3: Calculation
\(\dfrac{\Delta\rho}{\rho}\times100=4\%+3(2\%)=4\%+6\%=10\%\)
Final Answer:
The maximum permissible error in the density is 10%. \[ \boxed{\text{(C) }10\%} \]
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