A physical quantity `Q=(a^(2)b^(3)c^(5/2))/(x^(2)). ` If the percentage errors in the measurement of `'a','b','c'` and `x` are `1%,2%,3%,4%` reperctively, What is the percentage error in the measurement of `Q` ?

Options

A. `24%`
B. `12%`
C. `6%`
D. `8%`

Answer

A

Explanation

Here `Q=(a^(2)b^(3)c^(5//2))/(x^(2))`
`:.(dQ)/(Q)=(2da)/(a)+(3db)/(b)+(5)/(2)(dc)/(c )+2(dx)/(x)`
or `(dQ)/(Q)xx100=[2(da)/(a)+3(db)/(b)+(5)/(2)(dc)/(c )+2(dx)/(x)]xx100`
or percentage errors `Q` is
`=[2xx1+3xx2+(5)/(2)xx3+2xx4]`
`=23.5%~~24%`
`:.(a)` is correct.