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JEE Main 201815 April
Exam
JEE Main
Year
2018
Date
15 April
Subject
Physics
Chapter
Mathematics in Physics

JEE Main 2018 · 15 April · Physics · Mathematics in Physics

The relative error in the determination of the surface area of a...

The relative error in the determination of the surface area of a sphere is α\alpha. The relative error in the determination of its volume is

Options

  1. A32α\dfrac{3}{2} \alpha
  2. B23α\dfrac{2}{3} \alpha
  3. Cα\alpha
  4. D52α\dfrac{5}{2} \alpha

Correct answer

A. 32α\dfrac{3}{2} \alpha

Step-by-step solution

\Deltass=2×\Deltarr\dfrac{\Deltas}{s} = 2 \times \dfrac{\Deltar}{r}⇒\DeltaVV=3×\Deltarr⇒ \dfrac{\DeltaV}{V} = 3 \times \dfrac{\Deltar}{r}

∴\DeltaVV=32\Deltass\DeltaVV=32α\begin{array}{ll}∴ \dfrac{\DeltaV}{V} = \dfrac{3}{2}\dfrac{\Deltas}{s} \\ \dfrac{\DeltaV}{V} = \dfrac{3}{2} \alpha\end{array}
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