Question 187: 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: