Mathematics in Physics

JEE Main level, single correct, medium

107 of 121

Question 107 of 121

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

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Answer: (C) 32α\frac{3}{2} \alpha

Relative error in Surface area, Δss=2×Δrr=α\frac{\Delta \mathrm{s}}{\mathrm{s}}=2 \times \frac{\Delta \mathrm{r}}{\mathrm{r}}=\alpha and relative error in volume, Δvv=3×Δrr\frac{\Delta \mathrm{v}}{\mathrm{v}}=3 \times \frac{\Delta \mathrm{r}}{\mathrm{r}}
∴\therefore Relative error in volume w.r.t. relative error in area,
Δvv=32α\frac{\Delta \mathrm{v}}{\mathrm{v}}=\frac{3}{2} \alpha

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