The coefficient of linear expansion `'alpha`' of a rod of length `2` m varies with the distance x from the end of the rod as ` alpha = alpha_(0) + alpha_(1) "x" ` where `alpha_(0) = 1.76 xx 10^(-5) "^(@)C^(-1)"and" alpha_(1) = 1.2 xx 10^(-6)m^(-1) "^(@)C^(-1)`. The increase in the length of the rod. When heated through `100^(@)C` is :-

Options

A. `2`cm
B. `3.76`mm
C. `1.2`mm
D. None of these

Answer

B

Explanation

`Deltal = int`Expansion in dx =
`int[(alpha_(0) + alpha_(1)x)"dx"] DeltaT = 100int_(0)^(e) (1.76 xx 10^(-5) + 1.2 xx 10^(-6)x)` dx
=`100[(1.76 xx 10^(-5))x + (1.2 xx 10^(-6))(x^(2)/(2))]_(0)^(2)`
=`3.76`mm