TS EAMCET · Physics · Mathematics in Physics
A wooden cubical block of mass, \(m=20 \mathrm{~kg}\) is measured within an error of \(10 \mathrm{~g}\). Its side length, \(l=100 \mathrm{~cm}\) is measured within an error of \(1 \mathrm{~mm}\). Then, the relative error in the measurement of its density is
- A \(1.8 \times 10^{-2}\)
- B \(2.6 \times 10^{-2}\)
- C \(3.5 \times 10^{-3}\)
- D \(4.8 \times 10^{-3}\)
Answer & Solution
Correct Answer
(C) \(3.5 \times 10^{-3}\)
Step-by-step Solution
Detailed explanation
Density \(=\frac{\text { Mass }}{\text { Volume }} \Rightarrow \rho=\frac{m}{l^3}\) So, relative error in density is \(\frac{\Delta \rho}{\rho}=\frac{\Delta m}{m}+\frac{3 \Delta l}{l}\) Here, \(m=20 \mathrm{~kg}, \Delta m=10 \mathrm{~g}=10 \times 10^{-3} \mathrm{~kg}\),…
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