An experiment measure quantities x,y,z and then t is in calculate from the data as `t = (xy^(2))/(z^(2))` if perecentage error in x,y,z and are respectively `1% ,3%,2%` then percentage error in//is

Options

A. `10%`
B. `4%`
C. `7%`
D. `13%`

Answer

D

Explanation

`(Deltax)/x=1% =10^(-2)`
`(Deltay)/y=3% =3xx10^(-2)`
`(Deltaz)/z=2%=2xx10^(-2)`
`t=(xy^(2))/(z^(3))rArr (Deltat)/t=(Deltax)/x+(2Deltay)/y+(3Deltaz)/z`
`=10^(-2)+2xx3xx10^(-2)+3xx2xx10^(-2)`
`=13xx10^(-2)=13%`