Question

EXPLAIN PROPAGATION OF ERRORS CLEARLY 11TH STD


Addition​

Answer 1

Explanation:

If Q is some combination of sums and differences, i.e.

Q = a + b + · · · + c − (x + y + · · · + z), (1)

then

δQ =

p

(δa)

2 + (δb)

2 + · · · + (δc)

2 + (δx)

2 + (δy)

2 + · · · + (δz)

2. (2)

In words, this means that the uncertainties add in quadrature (that’s the fancy math word for the

square root of the sum of squares). In particular, if Q = a + b or a − b, then

δQ =

p

(δa)

2 + (δb)

2. (3)

Example: suppose you measure the height H of a door and get 2.00 ± 0.03 m. This means that

H = 2.00 m and δH = 0.03 m. The door has a knob which is a height h = 0.88 ± 0.04 m from the bottom

of the door. Then the distance from the doorknob to the top of the door is Q = H − h = 1.12 m. What

is the uncertainty in Q? Using equation (3),

δQ =

p

(δH)

2 + (δh)

2 (4)

=

p

(0.03 m)2 + (0.04 m)2 (5)

=

p

0.0009 m2 + 0.0016 m2 (6)

=

√

0.0025 m2 = 0.05 m. (7)

So Q = 1.12 ± 0.05 m