Identify the correct sequence for combining measurement uncertainties when evaluating…

PHYSICS · Single correct · CBSE · Physics · Units and Measurements · Units and Measurements

Problem

Identify the correct sequence for combining measurement uncertainties when evaluating the quantity

Z=(A+B)C^{2}

from independent measurements of

A, B

and

C

. (a) Add the relative uncertainties of

A

and

B

to obtain the relative uncertainty of

(A+B)

, then add twice the relative uncertainty of

C

to arrive at the relative uncertainty in

Z

. (b) Add the absolute uncertainties of

A,\,B

and twice that of

C

to form the combined absolute uncertainty, then divide the result by

Z

to obtain its relative uncertainty. (c) First add the absolute uncertainties of

A

and

B

to get

\Delta(A+B)

, divide this by

(A+B)

to convert it to a relative form, and finally add twice the relative uncertainty of

C

to obtain the relative uncertainty in

Z

. (d) Add the absolute uncertainties of

A

and

B

to get

\Delta(A+B)

, then multiply this result by

C^{2}

and quote the product as the absolute uncertainty in

Z