The co-efficient of thermal expansion of a rod is temperature dependent and is given by the formula `alpha = aT`, where `a` is a positive constant at T `"in"^(@)C`. if the length of the rod is l at temperature `0^(@)C`, then the temperature at which the length will be `2l` is

Options

A. `sqrt((ln2)/alpha)`
B. `sqrt((ln4)/alpha)`
C. `1/(alpha)`
D. `2/alpha`

Answer

B

Explanation

As, `dl=alpha l dT :. underset(l)overset(2l)(int) (dl)/(l) = a underset(0)overset(T)(int) T dT`
`1n 2 = a(T^2)/(2) :. T = [ (1n 4)/(a)]^(1//2)`.