When two measured quantities and with absolute uncertainties and are added to obtain

PHYSICS · Single correct · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

When two measured quantities

x

and

y

with absolute uncertainties

\Delta x

and

\Delta y

are added to obtain

z = x + y

, the absolute uncertainty

\Delta z

z

is (a)

\Delta z = \sqrt{\Delta x^{2} + \Delta y^{2}}

(b)

\Delta z = z\!\left(\dfrac{\Delta x}{x}+\dfrac{\Delta y}{y}\right)

(c)

\Delta z = \Delta x + \Delta y

(d)

\Delta z = \dfrac{\Delta x + \Delta y}{2}