A metallic rod 1 cm long with a square cross-section isheated through 1°C. If Young's modulus of elasticity ofthe metal is E and the mean coefficient of linearexpansion is alpha per degree Celsius, then thecompressional force required to prevent the rod fromexpanding along its length is : (Neglect the change of crosssectional area)

Thermal expansion in form of change in length 

l2 = l1(1+alpha*t)

Young’s modulus = E 

E = (F/A)/(l/L)

E = FL/Al

L = l + del l 

E = F (l+del l )/A* del l 

Find the value of F 

F = EA(alpha *t)/(1+ alpha *t)

 

Thermal expansion in form of change in length (Linear expansion) l 2 = l 1 ( 1 + α t ) l2=l1(1+αt) c h a n g e i n l e n g t h = ( l Δ t ) change in length=(lΔt) Δ t = ( t 2 − t 1 ) Δt=(t2−t1) Y o u n g ′ s M o d u l u s = E Young′s Modulus=E E = F A / l L E=FA/lL E = F L / A l E=FL/Al L = ( l + Δ l ) L=(l+Δl) L = l + Δ l L=l+Δl E = F A / l L E=FA/lL E = F L / A l E=FL/Al E = F ( l + Δ l ) A Δ l E=F(l+Δl)AΔl F = E A Δ l / ( l + Δ l ) F=EAΔl/(l+Δl) F = E A ( α t ) 1 + α t F=EA(αt)1+αt