Question

A physical quantity Q is found to depend on observables x, y and z, obeying relation Q=x3y2/z. The percentage error in the measurements of x, y and z are 1%, 2% and 4% respectively. What is percentage error in the quantity Q.​

Answer 1

Answer -

Suppose , $\rm x = \frac{ {a}^{n} }{b^m}$

Percentage error in value of x = n (percentage error in value of a) + m (percentage error in value of b)

For the given question -

$\rm Q = \dfrac{{x}^{3}{y}^{2}}{z}$

$\implies$Percentage error in x = 1%

$\implies$Percentage error in y = 2%

$\implies$Percentage error in z = 4%

Percentage error in Q = 3 ( percentage error in x ) + 2 ( percentage error in y ) + 1 ( percentage error in z )

Percentage error = 3 ( 1% ) + 2 ( 2% ) + 1( 4% )

Percentage error = 3% + 4% + 4%

Percentage error = 11%

$\boxed{\rm\pink{Percentage \:error\: in\: value\: of\: Q = 11\%}}$

Answer 2

Explanation:

Suppose , \rm x = \frac{ {a}^{n} }{b^m}x=

b

m

a

n

Percentage error in value of x = n (percentage error in value of a) + m (percentage error in value of b)

For the given question -

\rm Q = \dfrac{{x}^{3}{y}^{2}}{z}Q=

z

x

3

y

2

\implies⟹ Percentage error in x = 1%

\implies⟹ Percentage error in y = 2%

\implies⟹ Percentage error in z = 4%

Percentage error in Q = 3 ( percentage error in x ) + 2 ( percentage error in y ) + 1 ( percentage error in z )

Percentage error = 3 ( 1% ) + 2 ( 2% ) + 1( 4% )

Percentage error = 3% + 4% + 4%

Percentage error = 11%

\boxed{\rm\pink{Percentage \:error\: in\: value\: of\: Q = 11\%}}

PercentageerrorinvalueofQ=11%