Calculate Young's Modulus!

Classical Mechanics Level 5

The diameter of a wire of length 100 cm is measured with the help of a screw gauge. The main scale reading is 1mm and circular scale reading is 25. Pitch of the screw gauge is 1 mm and the total number of divisions on the circular scale is 100. The wire is used in an experiment for determination of Young's modulus of the wire by Searle's method. The following data are available:

Elongation in the wire $\Delta l$ is 0.125 cm under the tension of $50 N$ , least count for measuring normal length of wire is 0.01 cm and for elongation in the wire is 0.001 cm. The maximum error in calculating the value of Young's modulus (Y), assuming that the force is measured very accurately, is $\large \frac{8n}{10}$ %, where $n$ is very nearly an integer, then what is the value of $n$ ?

The answer is 3.00.

1 solution

Tanishq Varshney
Jun 13, 2015

$\large{Y=\frac{stress}{strain}}$

$\large{Y=\frac{4TL}{\pi D^{2} \Delta L}}$

$D=1.25~mm$ , $T=50~N$ , $\Delta L=0.125~cm$ , $L=1~m$

$Y=3.26\times 10^{10}~N/m^2$

$\large{\frac{\Delta Y}{Y}=\frac{2 \Delta D}{D}+\frac{\Delta L}{L}+\frac{\Delta(\Delta L)}{\Delta L}}$

$\Delta D=0.01~mm$ , $\Delta L=0.01~cm$ , $\Delta(\Delta L)=0.001~cm$

but the answer is not matching from this, Plz tell @Nishant Rai where is the problem

YOU ARE TAKING L IN (1m)METER AND (DELTA)L IN cm.

aryan goyat - 5 years, 7 months ago

Calculate Young's Modulus!

The answer is 3.00.

1 solution

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