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A physical quantity P is related to four...

A physical quantity P is related to four observables A, B, C and D as `P=4pi^(2)A^(3)B^(2)//(sqrt(C)D)`. The percentage error of the measurement in A, B, C and D are `1%, 3%, 2%` and `4%` respectively. The percentage error is `2a%` and absolute error in the quantity P is `b/2`. Find 'a' and 'b' if value of P is 3.57.

Text Solution

Verified by Experts

The correct Answer is:
`7, 1`
`P=(4pi^(2)A^(3)B^(2))/(sqrt(C)D)`
`((DeltaP)/P)%=[(3 Delta A)/A+(2 Delta B)/B+1/2(DeltaC)/C+(DeltaD)/D]%`
`=[3xx1+2xx3+1/2xx2+4]%`
`= 14 %`
`:. " "a=7`
`Delta P=Pxx14%=Pxx14/100`
`=3.57xx14/100=0.5=1/2`
`:." "b=1`
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