Question

a)if temperature increases what happens to youngs modulus? increase/decrease/remains same.
b)on hammering what happens to youngs modulus?
c) On increasing density what happens to youngs modulus ?
d) On increasing temperature what happens to modulus of rigidity ?
e) at melting point of any substance what is the value of youngs modulus?

Answer 1

Dear student,
a)
When heat is generated into the wire then the heat generated and the stored potential energy of the wire will be related as,
$heatgenerated=storedenergy$
In mathematical form we can write,
$ms\Delta \theta =\frac{1}{2}\times stress\times strain\times volume$
As, $stress=\frac{Mg}{A}$ and $strain=\frac{Mg}{YA}$ and $volume=LA$
Where,
$$\begin{gathered} m=mass \\ s=specificheat \\ \Delta \theta =temperature \\ M=mass \\ g=gravitationalforce \\ A=crosssectionalareaofthewire \\ Y=Yopung\text{'}smodulusofelasticity \\ \rho =density \end{gathered}$$

On rearranging the equation we get,
$\left(AL\rho \right)s\Delta \theta =\frac{1}{2}\times \frac{Mg}{A}\times \frac{Mg}{YA}\times LA$
that is,
$Y=\frac{{\left(Mg\right)}^2}{2A^2\rho s\Delta \theta }$
From above equation it can be concluded that young's modulus of elasticity is inversely proportional to the temperature. So, if the temperature is increased then the young's modulus of the wire will decreases.
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Regards