Question 215: Units , Dimensions and Error Analysis

Question

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

Accepted Answer

Relative error in the surface are of the sphere,
${{\Delta S} \over S}$ = 2 $ 	imes $ ${{\Delta r} \over r}$ = $ \propto $ (given)
Relative error in volume,
${{\Delta V} \over V}$ = 3 $ 	imes $ ${{\Delta r} \over r}$
= 3 $ 	imes $ ${1 \over 2}$ $ 	imes $ ${{\Delta S} \over S}$
= ${3 \over 2}$ $ 	imes $ $ \propto $
= ${3 \over 2}$  $ \propto $

Answer

${3 \over 2}\alpha $

Answer

${2 \over 3}\alpha $

Answer

${5 \over 2}\alpha $

Answer

$\alpha $

Units , Dimensions and Error Analysis

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

Choose the correct answer: