A physical quantity `rho` is calculated by using the formula `rho =(1)/(10)(xy^(2))/(z^(1//3))`, where x, y and z are experimentally measured quantities. If the fractional error in the measurement of x, y and z are `2%, 1%` and `3%`, respectively, then the maximum fractional error in the calculation of `rho` is

Options

A. 0.005
B. 0.05
C. 0.06
D. 0.07

Explanation

`epsilon=(xy^(2))/(10z^(1//3))`
Take log and differentiate,
`(Deltaepsilon)/(epsilon)=(Deltaex)/(x)+(2Deltay)/(y)-(1)/(3)(Deltaz)/(z)`
for maximum error,
`(Deltaepsilon)/(epsilon)=(Deltax)/(x)+2(Deltay)/(y)+(1)/(3)(Deltaz)/(z)`
`=2%+(2xx1%)+((1)/(3)xx3%)`
`=2%+2%+1%=5%`