Question 202: Units , Dimensions and Error Analysis

Question

A physical quantity P is described by the relation
P = a$$^{{\raise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}$$ b2 c3 d$$-$$4
If the relative errors in the measurement of a, b, c and d respectively, are 2%, 1%, 3% and 5%, then the relative error in P will be :

Accepted Answer

Given,
P = a$$^{{1 \over 2}}$$ b
2
c
3
d
$$-$$4
Relative error =
$${{\Delta P} \over P}$$ $$ 	imes $$ 100 = ($${1 \over 2}$$ $$ 	imes $$ $${{\Delta a} \over a}$$ + 2$${{\Delta b} \over b}$$ + 3$${{\Delta c} \over c}$$ + 4$${{\Delta d} \over d}$$) $$ 	imes $$ 100
= $${1 \over 2}$$ $$ 	imes $$ 2 + 2 $$ 	imes $$ 1 + 3 $$ 	imes $$ 3 + 4 $$ 	imes $$ 5
= 32%

Answer

8%

Answer

12%

Answer

32%

Answer

25%

Units , Dimensions and Error Analysis

A physical quantity P is described by the relation P = a$^{{\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}} b2 c3 d-$4 If the relative errors in the measurement of a, b, c and d respectively, are 2%, 1%, 3% and 5%, then the relative error in P will be :

Choose the correct answer: