question_answer

The coefficient of linear expansion for a certain metal varies with temperature as \[\alpha \](T). If L is the initial length of the metal and the temperature of metal is changed from\[{{\operatorname{T}}_{0}} to T \left( To > T \right)\] , then

A) \[\operatorname{L}={{L}_{0}}\int_{{{T}_{0}}}^{T}{\alpha \left( T \right)dT}\]

B) \[\operatorname{L}={{L}_{0}}\left[ 1+\int_{{{T}_{0}}}^{T}{\alpha \left( T \right)dT} \right]\]

C) \[\operatorname{L}={{L}_{0}}\left[ 1-\int_{{{T}_{0}}}^{T}{\alpha \left( T \right)dT} \right]\]

D) \[\operatorname{L}>{{L}_{0}}\]