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. `0.5%`
B. `5%`
C. `6%`
D. `7%`

Answer

B

Explanation

`(Delta zeta)/(zeta)xx100=((Deltax)/(x)+(2Deltay)/(y)+(1)/(3)(Deltaz)/(z))xx100`
`=2+2xx1+(1)/(3)xx3=5%`