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_(o)(1+alphaDeltaT)`
where `DeltaT` 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 `" "DeltaL = L_(t)-L_(o)=L_(o)alpha DeltaT`
where `alpha` is coefficient of linear expansion.
Young's modulus (Y) = `("Stress")/("Strain")=(F L_(o))/(A xx DeltaL)=(FL_(o))/(AL_(o)alpha DeltaT)prop(1)/(DeltaT)`
As, `" Y"prop (1)/(DeltaT)`
When temperature increases `DeltaT` increases, hence, Y decreases.