Home
Class 12
PHYSICS
Find the relative error in Z, if Z =(A^(...

Find the relative error in Z, if `Z =(A^(4)B^(1//3))/(CD^(3//2)` and the percentage error in the measurements of A,B,C and D are 4%,2%,3% and 1%, respectively.

Text Solution

Verified by Experts

`(DeltaZ)/Z=4((DeltaA)/A)+1/3((DeltaB)/B)+(DeltaC)/C+3/2((DeltaD)/D)`
Given that, `(DeltaA)/Axx100=4(DeltaB)/Bxx100=2,(DeltaC)/Cxx100=3`
and `(DeltaD)/Dxx100=1`
`therefore(DeltaZ)/Zxx100=(4xx4)+(1/3xx2)+3+(3/2xx1)`
`=16+2/3+3+3/2=21.16%`
The percentage error in the measurement of Z is 21.16%.
Therefore, the relative error in Z is 0.2116
Promotional Banner

Similar Questions

Explore conceptually related problems

In the measurement of a physical quantity X = (A^(2) B)/(C^(1//3) D^(3)) . The percentage erros introduced in the measurments of the quantities A,B,C and D are 2%,2%,4% and 5% respectively. Then the minimum amount of percentage of error in the meaurement fo X is contributed by

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?

In the measurement of a physical quantity X = (A^(2)B)/(C^(1//3)D^(3)) . The percentage errors introduced in the measurement of the quantites A,B,C and D are 1%, 3% , 4% and 5% respectively . Then the minimum amount of percenatage of error in the measurment of X is contributed by

A physical quantity X is give by the relation X = (2h^(3)I^(2))/(2sqrt(n)) The percentage error in the meansurement of k ,I,m and n are 1% ,2%, 3% and 4% respectively The value of X is uncertain by

A physical quantity z depends of four obserbles a, b, c and d, as z = (a^2b^(2/3))/(sqrtc d^3) . The percentages of error in the measurement of a,b,c and d are 2%, 1.5%, 4% and 2.5% respectively. The peracentage of error in z is :

A physcial quantity X is related to four measurable quantites a, b, c and d as follows : 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%, 3% and 4%, respectively. What is the percentage error in quantity X ? if the value of X calculated on the basis of the above relation is 2.763, to what value should you round off the result ?

A physical quantity X is given by X=(2k^(3)l^(2))/(msqrt(n)) The percentage error in the measurement of K,l,m and n are 1%,2%, 3% and 4% respectively. The value of X is uncertain by

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.

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% and 2%, 4% respectively. Determine the percenrage error & absolute error in the quantity P. Value of P is calculated 3.763.