A physical quantity Q is found to depend on observables x, y and z, obeying relation `Q=(x^(3)y^(2))/(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 ?

Options

A. 0.11
B. 0.04
C. 0.01
D. 0.03

Answer

A

Explanation

`Q=(x^(3)y^(2))/(z)`
The percentage error in the quantity Q is
`(DeltaQ)/(Q)xx100=(3 (Delta x)/(x)+2(Deltay)/(y)+(Deltaz)/(z))xx100`
`=3((Deltax)/(x)xx100)+2((Deltay)/(y)xx100)+(Deltaz)/(z)xx100`
`=3xx1%+2xx2%+4%=11%`