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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 l at temperature 00C,  then the temperature at which the length will be 2l is

a
ln2a
b
ln4a
c
1a
d
2a

detailed solution

Correct option is B

dl = lαdTdll=aTdT ∫l2ldll=∫0ToaT.dT ln ll2l= aT220To ln 2= aTo22 To=ln 4a

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