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A physical quantitiy X is related to fou...

A physical quantitiy X is related to four measurable quantities, a,b,c and d as give `X=a^(2)b^(3)c^(5//2)d^(-2)`. The percentage error in the measurement of `a,b,c` and d are 1%,2%,2% and 4% respectively. What is the percentage error in quantitiy X?

A

0.15

B

0.17

C

0.21

D

0.23

Text Solution

Verified by Experts

The correct Answer is:
C
As `X=a^(2)b^(3)c^(5//2)d^(-2)`
the percentage error in X is
`(DeltaX)/(X)xx100=[2((Deltaa)/(a))+3((Deltab)/(b))+(5)/(2)((Deltac)/(c))+2((Deltad)/(d))]xx100`
`=2xx1%+3xx2%+(5)/(2)xx2%+2xx4%=21%`
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