Question

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

Answer 1

Correct Answer - d
`(Delta x)/(x)= 1% = 10^(-2)`
`(Delta y)/(y)= 3% = 10^(-2)`
`(Delta z)/(z)= 2% = 10^(-2) rArr t = (xy^(2))/(z^(2))`
`(Delta t)/(t)= (Delta x)/(x)+(2Delta y)/(y)+(3 Delta z)/(z)`
`= 10^(-2) + 2xx 3 xx 10^(-2) + 3 xx 2 xx 10^(-2)`
`= 13 xx 10^(-2) = 13%`