Let `x={:[(a^(2)b^(2))/(c)]:}` be the physical quantity. If the percentage error in the measurement of physical quantities a,b, and c is 2,3 and 4 per cent respectively, then percentage error in the measurement of x is

Options

A. `7%`
B. `14%`
C. `21%`
D. `28%`

Answer

B

Explanation

Given
`x=(a^(2)b^(2))/(c)`
`(Deltax)/(x)=2(Deltaa)/(a)+2(Deltab)/(b)+(Deltac)/(c)`
`(Deltax)/(x)xx100=2((Deltaa)/(a)xx100)+2((Deltab)/(b)xxb)+((Deltac)/(c)xxc)`
Here, percentage error in a=2
Percentage error in b=3
Percentage error in c=4
`((Deltax)/(x)xx100)=2xx2+2xx3+4`
`=4+6+4=14%`