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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 $^{0} C .$ If the length of the rod is l at temperature $0^{0} C,$ then the temperature at which the length will be $3 l$ is

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detailed solution

Correct option is B

dl = lαdTdll=aTdT ∫l3ldll=∫0ToaT.dT ln ll3l= aT220To ln 3= aTo22 To=ln 9a

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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 3l is

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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 $^{0} C .$ If the length of the rod is l at temperature $0^{0} C,$ then the temperature at which the length will be $3 l$ is