The external and internal diameter of a tube are measured as (32 \pm 2)mm and (21 \pm 1)mm respectively. Determine the percentage error in the thickness of the tube.
A
27%
B
14%
C
9%
D
3%
Verified Correct Answer: A.
Physical Principles & Numerical Solution
The thickness of the tube is given by:
thickness = (external diameter − internal diameter) / 2
= (32 − 21) / 2
= 11 / 2
= 5.5 mm
Let t = thickness = \(\frac{(D − d)}{2}\), where D = external diameter and d = internal diameter.
The absolute error in thickness is found using the rules for propagation of errors (for subtraction and division by a constant):
\Deltat = \(\frac{(\DeltaD + \Deltad)}{2}\)
= \(\frac{(2 + 1)}{2}\) = \(\frac{3}{2}\)
=1.5 mm.
The percentage error in thickness is:
Percentage error = \(\frac{\Deltat }{\text{t}}\) \times 100%
= (\(\frac{1.5}{ 5.5}\)) \times 100%
= (\(\frac{15}{ 55}\)) \times 100%
= (\(\frac{3}{11}\)) \times 100% ≈ 27.27%
Source: Myschool Past Questions Archive (Record #27952)