Q85 / 90 · JEE Main 2018 (15 Apr) · Physics

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

Correct answer
A
$\frac{3}{2} α$
B
$\frac{2}{3} α$
C
$α$
D
$\frac{5}{2} α$

Solution

\frac{Δ s}{s} = 2 \times \frac{Δ r}{r}

\Rightarrow \frac{Δ V}{V} = 3 \times \frac{Δ r}{r}

\begin{array}{l} ∴ \frac{Δ V}{V} = \frac{3}{2} \frac{Δ s}{s} \\ \frac{Δ V}{V} = \frac{3}{2} α \end{array}

Hence, the correct answer is option: 'A'.

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