Caculate the compressional force required to prevent the metallic rod of length 1 cm and cross-sectional area A cm^(2) when heated through t^(@)C, from expanding along lengthwise. The young's modulus of elasticity of the metal is E and mean coefficient of linear expansion is alpha per degree celsius :

Caculate the compressional force required to prevent the metallic rod

1.	Caculate the compressional force required to prevent the metallic rod of length 1 cm and cross-sectional area A cm^(2) when heated through t^(@)C, from expanding along lengthwise. The young's modulus of elasticity of the metal is E and mean coefficient of linear expansion is alpha per degree celsius :
Answer» Solution :The change in natural LENGTH = `Delta1_(t)=1alphat` The natural length of rod at TEMPERATURE `t^(@)C` is `1+lalphat` The decrease in natural length due to developed stress = `Deltal` But the length of rod remains constant. `thereforeDelta1_(t)-Delta1=0""thereforeDelta1=Delta1_(t)=1alphat` `thereforeE=("stress")/("strain")=(F/A)/((-DeltaL)/(l+Deltal_(t)))` `thereforeF=(EADeltal)/(l+Deltal_(t))=(EADeltal_(t))/(l+Deltal_(t))=(-EA1alphat)/(l+lalphat)=-(EAalphat)/((1+alphat))` Here, negative sign INDICATES that the FORCES is compressive in nature.