This question considers aspects of a physical measurement performed to estimate

Question

This question considers aspects of a physical measurement performed to estimate by determining experimentally the circumference and diameter of a particular round object.

a) A group of students recored the measurements shown in the table.Estimate the circumference and diameter of the object along with the respective uncertainty. Express your results in a form that reflects both the expected value along with its uncertainty. Show birefly how you arrived at your results.

b) What value of is implied by the data? From the uncertainties in the diameter and circumference determine the uncertainty of the experimental value of . Is the experimental value consistent with that expected from mathematics? Explain.

c) The group who took the measurements also wishes to determine the area of the object considered using the formula A=0.25CD. What area and associated uncertainty are found? Show how you arrived at your answer.

d) Suppose one has access to several round objects of different size. Describe how plotting the circumference versus the diameter for the objects can be used to estimate . How might the uncertainty be assessed in this case?

Explanation / Answer

circmference =2pir =C

diameter=2r =D

area =pir2 =A

from these A=(1/4)CD

b)value of pi =39.2/12.5 =3.136

c)Area = pir2 =3.136 x (6.25)2 =122.5m2

d)draw a straight line taking Y axis as C and x axis as D

then slope of the line gives pi

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