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Q.

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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a

ln2a

b

ln4a

c

1a

d

2a

answer is B.

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Detailed Solution

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