The temperature of a wire is doubled. The Young's modulus of elasticity

Options

A. Will also double
B. Will become four times
C. Will remain same
D. Will decrease

Answer

D

Explanation

We know that with increase in temperature length of a wire changes as `L_(t)= L_(0) (1+ alpha Delta T)`
where `Delta T` is change in the temperature, `L_(0)` is original length, `alpha` is coefficient of linear expansion and `L_(t)` is length at temperature T . Now we can write `Delta L= L_(t) - L_(0) = L_(0) alpha Delta t`
Where `alpha` is coefficient of linear expansion. Young’s modulus `(Y)= ("Strees")/("Strain")= (FL_(0))/(A xx Delta L)= (FL_(0))/(AL_(0) alpha Delta T) prop (1)/(Delta T)`
As, `Y prop (1)/(Delta T)`
When temperature increases `Delta T` increases, hence, Y decrease.