Modulus of Elasticity

Modulus of clasticity It is the ratio of stress to the strain. X modulus of elasticity has same unit and cli- mension as that of stress unit = N/m2 Dimension = [ML'T2] E depenas on natural of material and temp- crature.

x6 doesn't depends on oli- Y/ F/A mension. 01/1 al i) young's modulus Y= F/A 01=21 of elasticity 1 - 1 Ratio of longitudinal = l/s stress to the longitu- when length is doubled olinal strain. Y=stress. Y= F young's modulus A of wire; Dl P Y= Fl l ADl Y= Fl Y= mgl w=mg falled AAl =F screater the youngs mo- Elongation of wire (Ad) clusus of elasticity, mat- crial is more clastic. of = mgl y Tir2 young's modulus of el- same articity is only for so- if force and materi- lias. as is same ,then along- *Steel is more epastic th- ation 'Al' is equal to an rubber. Al & & ri r2 % is for perfectly et- gid astic body is infinite, Elongation of wire due NOTE to it's own weight:- when length is dou- l bled, 1/2

y= Fl = mgD AAl 2A01 N/ PAlgl 2ADI y= pgl 201 01 = Pgl2 2Y

ii) Balk modulus of elasticity and nooning Bulk stress B = volumetric strain)

It is the ratio of bulk St- ress to the volumenic St- rain. F/A -Av V = - FV B= -PV AAV DV N/m' Butk modulus of solids, liquids, gases Bs >Bs > Bg perfect rigid body B=00 compressibility (c) = Reciproral of elast icity C= I = DV B PV my/ = N in2 'g > ' I >ls Fractional change in racius of sphere V= 4 Tir 7 3 DV 3Ar V o

1. DV = Dr 3 r 1/3 AV = Dr I V r B = PV - DV B = P - DV V Av = P V B I DV / P. 2 B I P = or 3 B P=mg r A 1 mg = Dr 3AB $20 d Rigidity modulus of elasticity Dx (ci) l (n) 5 = shecring stress shearing strain G= F/A AE 0

C = F AO G= F/A ony l * solids only; KY a = Fl A Ax 11