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Error and Uncertainty

A student did...

Question

A student did an experiment to determine the Youngs modulus $(Y)$ of a nylon thread, $2.00 m$ in length, using Searles method. A Vernier callipers having a least count of $0.01 m m$ was used to measure the diameter of the thread. The length and extensions were measured by using a scale with a least count of $1 m m$ . The data obtained by the student are shown in the table below. Assume the uncertainty in force to be $0.01 N$ .
Length of the thread $1994 m m$
Force $0.32 N$
Extension of the thread $95 m m$
Diameter of the thread $0.04 m m$
Choose the correct alternative(s).

The student reports

Y

to be about

5 G P a

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The reported uncertainty in

Y

54

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Measuring the extension using a travelling microscope with a least count of

0, 1 m m

would improve the accuracy of the result by at most

1

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The stress is

1.8 G P a

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Solution

The correct options are
A The student reports $Y$ to be about $5 G P a$
B The reported uncertainty in $Y$ is $54$ %
C Measuring the extension using a travelling microscope with a least count of $0, 1 m m$ would improve the accuracy of the result by at most $1$ %

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Length of the thread	$1994 m m$
Force	$0.32 N$
Extension of the thread	$95 m m$
Diameter of the thread	$0.04 m m$

The correct options are A The student reports Y to be about 5GPa B The reported uncertainty in Y is 54% C Measuring the extension using a travelling microscope with a least count of 0,1 mm would improve the accuracy of the result by at most 1%

The correct options are
A The student reports $Y$ to be about $5 G P a$
B The reported uncertainty in $Y$ is $54$ %
C Measuring the extension using a travelling microscope with a least count of $0, 1 m m$ would improve the accuracy of the result by at most $1$ %