Question

If X = 8.00 0.04 cm and Y = 4.00 0.04 cm,
then
should be expressed as
(1) 2.00 + 0.01
(2) 2.00 + 0.02
(3) 2.00 0.03
(4) 2.00 0.04​

Answer 1

Answer:

X/Y = 2.00 + 0.03 cm.

Explanation:

X= 8.00 +- 0.04

Y = 4.00 -+ 0.04

Now, X/Y = 8.00/4.00

 X/Y = 2.00

Let X/Y = D

But, We need to find the error in X/Y.

Relative error in D or X/Y = AX/X+ AY/Y

:. AD/D = 0.04/8+ 0.04/4

.:. Relative error in D or X/Y = 0.12/8 =

0.015

.:. AD = 0.03

..D =X/Y=2.00 -+ 0.03 cm.

Answer 2

answer : (2.00 ± 0.03)cm

explanation: given, X = (8.00 ± 0.04)cm and Y = (4.00 ± 0.04)cm

now, we have to find X/Y

first find value of X/Y for main reading then find error of X/Y.

X = 8.00 and Y = 4.00

then, X/Y = 8.00/4.00 = 2

Let X/Y = r then, r = 2. 00 and now we have to find ∆r

now using formula,

∆r/r = ∆X/X + ∆Y/Y

here, r = 2.00 , ∆X = 0.04, ∆Y = 0.04, X = 8.00 and Y = 4.00

now, ∆r/2 = 0.04/8 + 0.04/4

or, ∆r/2 = 0.04[1/8 + 1/4]= 0.04 × 3/8

or, ∆r = 0.08 × 3/8 = 0.03

hence, X/Y should be expressed as (r ± ∆r) =( 2.00 ± 0.03)cm