A metal rod of length L and cross-sectional area A is heated through T ^ C . What is the force required to prevent the expansion of the rod lengthwise? (Y= Young's modulus of material of the rod, = coefficient of linear expansion of the rod.)

Step-by-step solution

The increase in length due to heating is given by L = L ₀(1+ T ) or L - L ₀= L = L ₀ T To compress the rod by L , the force required is given by F = YA L L Substituting the value of L and L we get F = YA L ₀ T L _ o (1+ T ) = YA T 1+ T