Question

Two lengths x and y which are measured in an experiment are

Answer 1

\[x= ( 10.0 \pm 0.1 ) cm\] and\[y= (5.0\pm0.1)cm\]
Calculate the uncertainty in
a) (x+y)
b)(x-y)
c)xy
d) \[\frac{ x }{ y }\]

Answer 2

@Somy

Answer 3

alright look
you need to memorize this

In addition or subtraction= errors are added up
In multiplication or division= percentage errors are added up

Answer 4

okay..

Answer 5

x= 10.0 +- 0.1
y= 5.0 +- 0.1

Answer 6

a) 10+5= 15
0.1+0.1 =0.2
so 15+-0.2

Answer 7

uncertainty in A will be 0.2

Answer 8

same for B

Answer 9

b) 10-5=5
0.1+0.1=0.2

Answer 10

yes thats right :)
the q is asking for uncertainty alone so it'll be 0.2

Answer 11

now C

Answer 12

do u know how to find %error?

Answer 13

% error= (error/actual value) *100

Answer 14

get it for both x and y

Answer 15

can u show me show me the working for c)

Answer 16

ok
% error in X= (0.1/10)* 100= 1%
% error in Y= (0.1/5)*100= 2%
so in multiplication or division % errors are added up
so % error= 1+2= 3%

now C) xy = 10*5= 50

50----100%
X-----3%
X= 50*3/100
X= 1.5
thus uncertainty in C is 1.5

Answer 17

get it?

Answer 18

Trying to undertand...

Answer 19

alright look
the value given for X= 10.0 +-0.1
right?

Answer 20

yes

Answer 21

0.1 is error right?

Answer 22

ys

Answer 23

ok so to find % error we have a formula

%error= error/actual value *100=
actual value in case of X is 10
get it?

Answer 24

ys

Answer 25

now whatever type of calculation that it is
addition, subtraction, multiplication or division
ACTUAL values do them

Answer 26

meaning 10 in case of X and 5 in case of Y

Answer 27

clear?

Answer 28

ys

Answer 29

the errors of X and Y do not take part in actual calculation
meaning they don't take part in addition, subtraction, multiplication or division

Answer 30

errors have their own rule

When its addition or subtraction between the actual values
errors of actual values will ALWAYS ADD UP

Answer 31

ok

Answer 32

now when its multiplication or division between actual values
PERCENTAGE ERRORS will ALWAYS ADD UP

Answer 33

get it?

Answer 34

yes

Answer 35

alright so do u understand the calculation now?

Answer 36

ys
for d) its 0.06
is it so

Answer 37

when you find % error, and now want to find uncertainty
what you do is that you take a product of multiplication or division of actual values as 100% and uncertainty is % error that you found

Answer 38

Okay

Answer 39

yup that's right)

Answer 40

Thanks for the explanation
@Somy

Answer 41

you are welcome :)