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If X=(a^(3)b^(2))/(sqrt(c)d) and percent...

If `X=(a^(3)b^(2))/(sqrt(c)d)` and percentage errors in a, b, c and d are `1%, 2%, 4%` and `4%` respectively, then the error in X will be

A

`10%`

B

`11%`

C

`13%`

D

`5%`

Text Solution

Verified by Experts

The correct Answer is:
C
`X=(a^(3)b^(2))/(sqrt(c)d)`
`therefore` the relative error in X is
`therefore (DeltaX)/(X)=3(Deltaa)/(a)+2(Deltab)/(b)+(1)/(2)(Deltac)/(c)+(Deltad)/(d)`
(Errors as added)
`therefore` % error in the measurement of X will be
`(DeltaX)/(X)xx100=3(Delta)/(a)xx100+2(Deltab)/(b)xx100+(1)/(2)(Deltac)/(c)xx100+(Deltad)/(d)xx100`
`=3xx1%+2xx2%+(1)/(2)xx4%+4%`
`=3%+4%+2%+4%=13%`
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