Question:
The maximum error in the measurement of the density and mass of the uniform cube are 8% and 2% respectively. Hence, the maximum error in the measurement of length will be
The maximum error in the measurement of the density and mass of the uniform cube are 8% and 2% respectively. Hence, the maximum error in the measurement of length will be
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Density = mass / L^3, so the percentage error in density is that of mass plus 3 times that of length.
Updated On: Oct 1, 2026
- \(2\%\)
- \(4\%\)
- \(6\%\)
- \(8\%\)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
For a cube of side \(L\) and mass \(M\), the density is \(\rho = \dfrac{M}{L^3}\). In the maximum error method, the percentage errors of the factors add up, each multiplied by the power of its quantity.
Step 2: Key Formula or Approach:
\[ \frac{\Delta\rho}{\rho} = \frac{\Delta M}{M} + 3\,\frac{\Delta L}{L} \]
Step 3: Detailed Explanation:
Given \(\dfrac{\Delta\rho}{\rho} = 8\%\) and \(\dfrac{\Delta M}{M} = 2\%\).
\[ 8 = 2 + 3x \Rightarrow 3x = 6 \Rightarrow x = 2\% \]
So the maximum error in the measurement of the length is 2 percent. Option (B) 4 % would need the density error to be 14 %. Option (C) 6 % and (D) 8 % ignore the power 3.
Final Answer:
The maximum error in length is 2 %, option (A). \[ \boxed{2\% \text{ (A)}} \]
For a cube of side \(L\) and mass \(M\), the density is \(\rho = \dfrac{M}{L^3}\). In the maximum error method, the percentage errors of the factors add up, each multiplied by the power of its quantity.
Step 2: Key Formula or Approach:
\[ \frac{\Delta\rho}{\rho} = \frac{\Delta M}{M} + 3\,\frac{\Delta L}{L} \]
Step 3: Detailed Explanation:
Given \(\dfrac{\Delta\rho}{\rho} = 8\%\) and \(\dfrac{\Delta M}{M} = 2\%\).
\[ 8 = 2 + 3x \Rightarrow 3x = 6 \Rightarrow x = 2\% \]
So the maximum error in the measurement of the length is 2 percent. Option (B) 4 % would need the density error to be 14 %. Option (C) 6 % and (D) 8 % ignore the power 3.
Final Answer:
The maximum error in length is 2 %, option (A). \[ \boxed{2\% \text{ (A)}} \]
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