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

`epsi = (xy^(2))/(10z^(1//3)) rArr epsi prop x^(1) y^(2)z^(-1//3)`
`rArr (Delta epsi)/(epsi) xx 100= ( (Delta x)/(x) + 2( Delta y)/(y) + (1)/(3) (Delta z)/(z)) xx 100`
`= 2% + (2 xx 1%) + ((1)/(3)xx 3%)`
`= 2% + 2% + 1% = 5%`