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The co-efficient of thermal expansion of a rod is temperature dependent and is given by the formula $α = a T,$ where a is a positive constant and T in $^{0} C .$ If the length of the rod is $l$ at temperature $0^{0} C,$ then the temperature at which the length will be $2 l$ is

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detailed solution

Correct option is B

expansion dl=lαdthere α=atdl=l at dtdll=atdt ∫l2ldll=∫0tatdt ln ll2l=at22 ln2=at22 ln4a=t2 t=ln4a

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The co-efficient of thermal expansion of a rod is temperature dependent and is given by the formula α=aT, where a is a positive constant and T in 0C. If the length of the rod is lat temperature 00C,then the temperature at which the length will be 2l is

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Ready to Test Your Skills?

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The co-efficient of thermal expansion of a rod is temperature dependent and is given by the formula $α = a T,$ where a is a positive constant and T in $^{0} C .$ If the length of the rod is $l$ at temperature $0^{0} C,$ then the temperature at which the length will be $2 l$ is