JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
The relative error in the determination of the surface area of a sphere is \(\alpha \). Then the relative error in the determination of its volume is
- A \(\frac{2}{3}\alpha \)
- B \(\frac{5}{2}\alpha \)
- C \(\frac{3}{2}\alpha \)
- D \(\alpha \)
Answer & Solution
Correct Answer
(C) \(\frac{3}{2}\alpha \)
Step-by-step Solution
Detailed explanation
\begin{array}{l} {\mathop{\rm Re}\nolimits} lative\,\,eroor\,\,in\,\,surface\,\,area,\\ \frac{{\Delta s}}{s} = 2 \times \frac{{\Delta r}}{r} = \alpha \,and\,relative\,error\,in\\ volume,\,\frac{{\Delta v}}{v} = 3 \times \frac{{\Delta r}}{r}\\ \therefore \,{\mathop{\rm…
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